iWM«) iJ.'»i)i!,'v iifi;il':;i:^ ■ ili la-iiS''^ ilMiliteiS:,.... A SYSTEM OF GEOMETRY AND TRIGONOMETRY, WITH A TREATISE OJT SURTEYING? COMPRISING VARIOUS METHODS OF TAKING THE SURVEY OP A FIELD, WITH DIRECTIONS FOR PROTRACTING AND FINDING AREAS : IN WHICH, ALSO, THE PRINCIPLES OF RECTANGUIiAR SURVEYING, BY WHICH AREAS MAY BE ACCURATELY CALCULATED WITH- OUT PLOTTING, ARE FULLY EXPLAINED : WITH A COMPLETE SERIES OF MATHEMATICAL TABLES, AND THE NECESSARY EXPLANATIONS, BY ABEI. FMNT, A. M. WITH IMPROVEMENTS BY GEORGE GILLET, SURVEYOR GENERAL OF CONNECTICUT. SIXTH SDITXON, REVISED AND ENLARGED, BY THE ADDITION OP COPIOUS NOTES AND ILLUSTRATIONS, AND A CONCISE TREATISE OI^LOGARITHMS, BY FKEDERIC A. P, BARNARD, A. B, INSTRUCTOR IN MATHEMATICS IN THE HARTFORD GRAMMAR SCHOOL, AND AUTHOR OF A TREATISE ON ARITHMETIC. ) HARTFORD : PUBLISHED BY COOKE & CO. FOR SALE BY THE PRINCIPAL BOOKSELLERS IN THE U. STATES. 1830. DISTRICT OF CONNECTICUT, ss. Be it Remembered, TLat on the second day of August, in J^, S» ^e fifrr-fifth year of the Independence of the United States of America. Oliver D. Cooke of the said District, hath deposited in this Office, the title of a book, the ri^ht whereof he claims as pro- prietor, in the words following to wit : '• A system of Geometry and Trigonometry, with a Treatise on Surreying ; comprising various methods of taking the survey of a field, with directions for protracting and finding areas ; in which, also, the principles of Rectangular Sur- veying, by which Areas may be accurately calculated without plotting, are fully explained : with a complete series of Matheraatical Tables, and the necessary explanations. By Abel Flint. A. M. With im- provements by George Gillet, Surveyor General of Connecti- cut. Sixth edition, revised and enlarcfed, by the addition of copi- ous notes and illustrations, and a concise Treatise on Logarithms, by Frederic A. P. Barnard, A. B. instructor in Mathematics in the Hart- ford Grammar School, and Author of a Treatise on Ariihinetic.*' In conformity to the act of Congress of the United States, entitled," An act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the times therein mentioned." And also to the act entitled. *' An act supplementary to an act, entitled. ' An act for the encouragement of learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the times therein men- tioned,' -- and extending the benefits thereof to the arts of designing, engraving, and etching historical, and other prints. CHARLES A. LXGERSOLL, Ckrk ofihi District of Conneciicut A true copv of record, examined and sealed bv me, CHARLES A. INGERSOLL, CUrk ofihi. JJistrict of Conntciicui. #^^ ^ ^. S-^87SP^ A DVERTISEMENT TO THE SIXTH EDITIOJ^. The original compiler of the following work designed, in preparing it, to furnish a plain and concise system of prac- tical SURVEYING, for the use of practical men. That he did not fail of success, has been sufficiently proved, by the high estimation in which this treatise has been, and is, at the present time, held by surveyors, and by the continued and increasing demand for it, from the public. In the present edition, the publishers have used every exertion to render it still more worthy of patronage. The valuable articles furnished to the fifth edition of the work, last published, by George Gillet, Esq., Surveyor General of the state of Connecticut, are retained in this. They will be found to contain a system of useful instructions for the practical surveyor, which cannot be elsewhere found. Additional matter has likewise been inserted in the present edition. These additions, when entirely independent of any thing previously contained in the book, or when substituted as an improvement for something omitted or altered, are inclosed in brackets, or are inserted in the form of a note at the foot of the page. Omissions, and alterations from the original work, however, are very few, and have only been made, where they were demanded by obvious necessity. Alterations in phraseology , will be found more numerous, and these have been made, wherever it was believed that they would either render the meaning more clear, or the language more concise. In this respect, the present edition will be found decidedly improved. iv ADVERTISEMENT. Prefixed to the tables will be found a brief explanation of the nature and use of logarithms. It has been a defect in former editions, that this subject has not been more fully treated. A very distinguishing feature, likewise, of the present edi- tion, is the introduction of a new and elegant set of tables, more extensive and on plainer type than those which have before been attached to the work. The decimals are carried to six figures, instead of five, as formerly, and a column of difi'erences is added, for the purpose of finding intermediate numbers. For many purposes, sufficient accuracy may be perhaps attained by the use of logarithms, extending only to five, or even four decimal places, but others v>ill likewise occur, in the experience of every surveyor, in which such logarithms will not answer the purpose. But if logarithms are carried to six places, they may be taken to as few, or as many, within that limit, as is desired. The above constitute the principal peculiarities of the present edition. Hartford, Augfust 2nd. 1830. PREFACE TO THE FIRST EDITIOX. The following work is chiefly a compilation from other Books ; and but very little new is added, except a more full explanation, than has yet been published, of Rectangular Surveying, or the method of calculating the area of fields arithmetically, without drawing a plot of them and measui'ing with a scale and dividers, as has been the com- mon practice ; and also a more particular explanation of the use of natural sines than is contained in most mathematical books. The compiler has endeavoured to render this work so easy and in- telligible that a learner will require but little assistance from an In- structer, except with regard to the construction and use of mathemati- cal and surveying instruments. Before, however, he enters on the study of this book, he must be well acquainted with common Arithme- tic, with decimal fractions, and the square root ; and he must also know the various characters or marks used in Arithmetic. A surveyor will doubtless find many questions arise in the course of his practice, for the solution of which, no particular directions are here given ; nor is it possible to give directions for every case that may occur. In all practical sciences much must be left to the judgment of the practitioner, who, if he is well acquainted with the general princi- ples of his art, will readily learn to apply those principles to particular cases. The primary design of this treatise is to teach common Field Survey- ing ; at the same time it contains the elements of Surveying upon a larger scale ; and the system of Geometry and Trigonometry with which it is introduced, with the problems for the mensuration of superficies, as also the mathematical tables at the end, will be found useful for many other purposes. It would be well, therefore, for those who do not intend to become practical surveyors to acquaint themselves with what is here taught ; and v/itli this view the following work is very proper to be in- troduced into academies and those higher schools which are designed to fit young men for active business in life. Indeed every person who frequently buys and sells land should learn to calculate the contents of a field arithmetically ; a knowledge which may be acquired in a very little time, from the particular explanation here given of that method. Notwithstanding the many books already published on the subjects here treated upon, it was thought a work of this kind was really want- ed, and that if judiciously executed it would be useful. It is more par- ticularly necessary at the present time in Connecticut, as the legisla- ture of the State have lately enacted a law on the subject of surveying, hi consequence of which more attention must be paid to the theory of that art than has been common. These considerations induced the compiler to select from various publications what appeared to him important ; and to arrange the whole in a method best adapted, in his view, for teaching that useful art. How far he has succeeded in his endeavours to simplify the sub- ject, and render it easy to the learner, must be submitted to the test of experience. A GEXERAL VIEW OF THE CONTENTS OF THIS WORK. Tee system of Geometry is divided into two parts. The first con- tains g-eometrical definitions respectin?^ lines, angles, saperficies, A:c. The second part contains a number of geometrical problems necessary for Trig-onometry and Sarreying. The system of Trigonometry is also divided into two parts : and teaches the solution of questions in right and oblique angled trigonom- etiy, by logarithms and also by natural sines. The treati^ on Surveying is divided into three parts. Part first treats of measaxing land, and is divided into three sections. The first contains several problems respecting mensuration, and for finding the area of various right-lined figures and circles. The second section teaches different methods of taking the Survey of fields ; also to protract them, and find their area in the manner com- monly practised, and likewise by arithmetical and trigonometrical cal- culations, without measaiing diagonals and perpendiciiars with a scale and dividers ; interepeareed with sundry useful rules and directions. The tliird section is a particular explanation and demonstration of Rectasgllab. SrRVETixG, or the method of computing the area of fields fi-om the field notes, by mathematical tables, without the necessi- ty of plotting the field. To this section is added a useful problem for ascertaining ihe true area of a field which has been measured by a chain too long or too short. Part second treats of laying oot land in various shapes. Part third contains sundry problems and rules for dividing land and determining the true course and distance of dividing lines, or from one part of a field to another. To this is added an appendix concerning die variation of the compass and attraction of the needle : also, a rule to fed the di^erence between the prf^sent variation, and that at a time wljem a tract was formerly surveyed, in order to trace or ran out the oriainal lines. The mathematical tables, are a traverse table, or table of difference of latitude and departure, calculated for every degree and quarter of a degree, and for any distance up to 30 ; a table of natural sines calcula- ted for exerj minute ; a table of logarithms comprised in four pages, yet suffidently extensive for common use ; and a table of logarithmic or artificial sines, tansrents. and secants, calculated for every 5 minutes of a degree. To these tables are prefixed particular explanations of the manner of using them-* * This view of the contents was drawn up by Mr. Flint, and refers of course to the original edition. ERRATA. Page lb, line 14 from top, for oMruse, read oUuse, 19, fig. 38, traaspQBe letters A aod C. 77, m ^ sale at die loot cf 1^ page, strike out tlie letter D, afier 130.5. GEOMETRY. GEO-METRY is a Science which treats of the properties of magnitude. PART I- Geometrical Definitions. 1. A point is a small dot ; or, mathematically considered. is that which hasnopEirts, being of itself indivisible . 2. A line has length but no breadth. 3. A superficies or surface, called also area, has length and breadth, but no thickness. 4. A solid has length, breadth, and thickness. 5. A right line is the shortest that can be draisna between two points. Fi£. 1. 6. Th'e inclination of two lines meeting one another, or the opening between them, is called an angle. Thus at B. Fig. 1. is an ansrle. formed bv the meeting of the lines AB and BC. 7. If a right hne CD. Fig. 2. fall upon another right line AB, so as to incline to neither side, but make the angles on each side equal, then those angles are called ri^ht angles ; and the line CD is said to be per- pendicular to the other line. B Fig. 2. D -B 10 GEOMETRY. Fig. 3. 8. An obtuse angle is greater than a right angle : as ADE. Fig. 3. 9. An acute angle is less than a right angle; as EDB. Fig.S. Note. When three letters are used to express an angle. the middle letter denotes the angular point. Fi^. 4. 10. A circle is a round figure, bounded by a single line, in every part equally distant from some point,, which is called the cen- tre. Fig. 4. 11. The circumference or periphery of a circle is the bounding line ; as ADEB. Fig. 4. 12. The radius of a circle is a line drawn from the centre to the circumference: as CB. Fig. 4. Therefore all radii of the same circle are equal. 13. The diameter of a circle is a right line drawn from one side of the circumter- ence to the other, passing through the centre; and it divides the circle into two equal parts, called semicircles ; as AB or DE. Fig. 5. 14. The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, calied minutes ; and each minute into 60 equal parts, called seconds : and these into thirds, 6z ig. D. Note. Since all circles are divided into the same number of degrees, a degree is not to be accounted a quantitv of any determinate length, as so many inches or feet. d:c. but is always to be reckoned as being the 360th part of the circumference of any circle, without regardino- the size of the circle. 15. An arc of a circle is any part of the circumference ; as BF or FD. Fig. 5 : and is said to be an arc of as many de^ grees as it contains 360th parts of the whole circle. GEOMETRY. 11 Fig, 6, 16. A chord is a right line drawn from one end of an arc to the other, and is the measure of the arc ; as HG is the chord of the arc HIG. Fis. 6. Note. The chord of an arc of 60 degrees is equal in length to the radius of the circle of which the arc is a part. 17. The segment of a circle is a part of a circle cut off by a chord ; thus the space comprehended between the arc HIG and the chord HG is called a segment. Fig. 6. 19. A sector of a circle is a space contained between two radii and an arc less than a semicircle ; as BCD or ACD. Fig. 6. 20. The sine of an arc is a line drawn Fig, 7. from one end of the arc, perpendicular to the radius or diameter drawn through the other end : or, it is half the chord of double the arc ; thus HL is the sine of the arc HB. Fig. 7. 21. The sines on the same diameter in- crease in length till they come to the cen- tre, and so become the radius, after which they diminish. — Hence, it is plain that the sine of 90 degrees is the greatest possible sine, and is equal to the radius. 22. The versed sine of an arc is that part of the diameter or radius which is between the sine and the circumference ; thus LB is the versed sine of the arc HB. Fig. 7. 23. The tangent of an arc is a right line touching the circumference, and drawn perpendicular to the diameter ; and is terminated by a line drawn from the centre through the other end of the arc ; thus BK is the tangent of the arc BH. Fig, 7. Note. The tangent of an arc of 45 degrees is equal in length to the radius of the circle of which the arc is a part. 24. The secant of an arc is a line drawn from the centre 12 GEOIETRY. through one end of the arc till it meets the tangent ; thus CK is the secant of the arc BH. Fig. 7. '25. The complement of an arc is what the arc wants of 90 degrees, or a quadrant : thus HD is the complement of the arc BH. Fig. 7. 26. The supplement of an arc is what the arc wants of ISO degrees, or a semicircle ; thus ADH is the supplement of the arc BH. Fig. 7. [Note. It will be seen, by reference to Fig. 7, that the sine of any arc is the same as that of its supplement. So like- wise, the tangent and secant of imy arc are used also for its supplement.] 27. The sine, tangent or secant of the complement of any arc is called the co-siue, co-tangent, or co-secant of the arc ; thus, FH is the sine, DI the tangent, and CI the secant of the arc DH ; or they are the co-sine, co-tangent, and co-se- cani of the arc BH. Fig. 7. [The terms sine, tangent and secant, are abre\iated thus : sin. tan. and sec. So llke^Tise, co-sine, co-tangent, and co- secant, are written co-sin, co-tan. and co-sec] 28. The measure of an angle is the arc of a circle contain- ed between the two lines which form the angle, the angular point being the centre ; thus, the angle HCB. Fig. 7. is mea- sured by the arc BH : and is said to contain as many degrees as the arc does. Note An angle is esteemed greater or less according to the opening of the lines which form it, or as the arc in- tercepted by those Unes contains more or fewer degrees. Hence it maybe observed, that the size of an angle does not depend at all upon the length of the including lines ; for all arcs described on the same point, and intercepted by the same right lines, contain exactly the same num- ber of degrees, whether the radius be longer or shorter. 29. The sine, tangent, or secant of an arc is also the sine, tancjent, or secant of the angle whose measure the arc is. Fig. 8. A^ B 30. Parallel lines are such as are equal- ly distant from each other; as AB and ^ j^ CD. Fig. 8. i^ 13 GEOMETRY. 13 31. A triangle is a figure bounded by three lines ; as ABC. Fig. 9. 32. An equilateral triangle has its three sides equal in length to each other. Fig. 9. 33. An isoceles triangle has two of its sides equal. Fig. 10. Fig. 11. Fig. 12 Fig. 13. 34. A scalene triangle has three unequal sides. Fig. 11. 35. A right angled triangle has one right angle. Fig. 12. 36. An obtuse angled triangle has one obtuse angle. Fig. 13. 37. An acute angled triangle has all its angles acute. Fig. 9, or 10. 38. Acute and obtuse angled triangles are called oblique angled triangles, or simply oblique triangles ; in which the lower side is generally called the base and the other two, legs. 39. In a right angled triangle the longest side is called the hypothenuse, and the other two, legs, or base and perpendic. lilar. B2 14 GEOMETRY. Note. The three angles of every triangle being added to- gether will amount to 180 degrees ; consequently the two acute angles of a right angled triangle amount to 90 degrees, the right angle being also 90. Fig. 14. 40. The perpendicular height of a trian- gle IS a line drawn from one of the angles perpendicular to its opposite side ; thus, the dotted line AD. Fig. 14. is the perpendicu- lar height of the triangle ABC. -p Note. This perpendicular may be drawn from either of the angles ; and whether it falls within the triangle, or on one of the lines continued beyond the triangle, is im- material. Fig. 15. 41. A square is a figure bounded by four equal sides, and containing four right angles. Fig, 15. 42c A rectangle* is a figure bounded by four sides, the opposite ones being equal and the angles right. Fig. 16. Fig. 16. Fig. 17. 43. A rhombus is a figure bounded by four equal sides, but has its angles oblique. Fig. 17. Fig. 18. 44. A rhomboid is a figure bounded by four sides, the opposite ones being equal, but the angles oblique. Fig. 18. * In previous editions, thia figure is denominated a parallelogram. The phr&seologjr employed bj modern writers, is here adopted.^-En. GEOMETRY. 15 [45. Any four-sided figure, having its opposite sides paral- lel, is called a parallelogram. Figs. 15, 16, 17, and 18.] 46. The perpendicular height of a parallelogram is a line drawn from one of the angles to its opposite side ; thus, the dotted lines AB. Fig, 17. and Fig. 18, represent the perpen- dicular height of the rhombus and rhomboid. Fig. 19. 47. A trapezoid is a figure bounded by four sides, two of which are parallel though of unequal lengths. Fig. 19. andi^i^. 20. / \ Fig. 20. Note. Fig. 19. is sometimes called a right angled trape- Fig. 21. zium. 48. A trapezium is a figure bounded by four unequal sides Fig. 21. 49. A diagonal is a line drawn between two opposite angles ; as the line AB. Fig. 21. Jl 50. Figures which consist of more than four sides are caK led polygons ; if the sides are equal to each other they are cal- led regular polygons, and are sometimes named from the num- ber of their sides, as pentagon, or hexagon, a figure of five or six sides, (fee. ; if the sides are unequal, they are called ir- regular polygons. 16 GEOMETRY. PART II. Geometrical Problems. Fig. 22. C PROBLEM I. To draw a line parallel to another line at any given distance ; as at the point D, to make a line, parallel to the ^- S.. .. -' lineAB. Fig. 22, ^ ^ With the dmders take the nearest distance between the point D and the given Une AB ; with that distance set one foot of the dividers any where on the line AB, as at E, and draw the arc C ; through the point D draw a line so as just to touch the top of the arc C. A more convenient way to draw parallel lines is with a parallel rule. [The parallel rules, however, found in <;ases of mathematical instruments, are often inaccurate.] PROBLEM II. To bisect agivenline or, to find the middle of it. Fig. 23. Fig. 23. IE -B Open the dividers to any convenient distance, more than half the given line AB, and with one foot in A, describe an arc above and below the line, as at C and D ; with the same distance, and one foot inB, describe arcs to cross the former; lay a rule from C to D, and where the rule crosses the line. as at E, will be the middle. Fig. 24. PROBLEM in. To erect a perpendicu. - /■ larfrom the end, or any part of a given line. Fig. 24. GEOMETRY. 17 Open the dividers to any convenient distance, as from D to A, and with one foot on the point D, from which the perpen- dicular is to be erected, describe an arc, as AEG ; set off the same distance AD, from A to E, and trom E to G ; upon E and G describe two arcs to intersect each other at H ; draw a Hne from H to D, and one line will be perpendicular to the other. Note. There are other methods of erecting a perpendicu- lar, but this is the most simple. Fig. 25. PROBLEM IV. From a given point as at C, to drop a perpendicular on a , given line AB. Fig 25. ^_ P With one foot of the dividers in C describe an arc to cut he given line in two places, as at F and G ; upon F and G describe two arcs to intersect each other below the line as at D ; lay a rule from C to D and draw a line from C to the giv- en line. Perpendiculars may be more readily raised and let fall, by a small square made of brass, ivory, or wood. Fig, 26. PROBLEM V. To male an angle at E, / equal to a given angle ABC. Fig. 26. . / Open the dividers to any convenient distance, and with one foot in B describe the arc FG ; with the same distance and one foot in E, describe an arc from H ; measure the arc FG and lay off the same distance on the arc from H to I • draw' a line through I to E, and the angles will be equal. Fig. 27. PROBLEM VL To make an acute an- gle equal to a given number of degrees, sup. / pose 36. Fig. 27. • / A IS GEOMETRY. Draw the line AB of any convenient length ; from a scale of chords take 60 degrees with the dividers, and with one foot in B describe an arc from the line AB ; from the same scale take the given number of degrees, 36, and lay it on the arc from C to D ; draw a line from B through D, and the angle at B will be an ano;le of 36 decrees. Fig. 28. PROBLEM VII. To male an ohtuse an- \ ^ C gle, suppose of llO degrees. Fig. 28. V-— ^l"**^--. B Take a chord of 60 degrees as before, and describe an arc greater than a quadrant ; set off 90^^grees from B to C, and from C to E set off the excess abo"^ 90, which is 20 ; draw aline from G through E, and the angle will contain 110 de- grees. [It is best, however, in making obtruse angles, to take from the scale the chord of half the angle, and set it off twice. This will save taking two separate chords.] Note. In a similar manner angles may be measured : that is, with a chord of 60 degrees describe an arc on the an- gular point, and on a scale of chords measure the arc in- tercepted by the lines forming the angle. Amore convenient method of making and measuring angles is to use a protractor instead of a scale and dividers. Fis. 29. B PROBLEM VIII. To make a triangle j^ of three given lines, as BO, BL, LO. Fig. 29, any two of which are greater than the third. Draw the line BL from B to L ; from B, with the length of the line BO, describe an arc as at O ; from L, with the length of the line LO, describe another arc to intersect the former ; from O draw the lines OB and OL, and BOL will be the triangle required. GEOMETRY. 1» PROBLEM IX. To make a right an- gled triangle, the hypothenxise and angles being given. Fig, 30. Suppose the hypothenuse CA 25 rods or chains, the angle at C 35° 30' and consequently the angle at A 54^ 30\ See note after the Sdth Geometrical Definition. Note. When degrees and minutes are expressed, they are distinguished from each other by a small cipher at the right hand of the degrees, and a dash at the right hand of the minutes ; thus 35° 30' is 35 degrees and 30 min- utes. Draw the line CB an indefinite length ; at.C make an an- gle 35° 30' ; through where that number of Degrees cuts the arc draw the line CA 25 rods, which must, be taken from some scale of equal parts ; drop a perpendicular from A to B, and the triangle will be completed, [A scale of equal parts may be found on one side of Gun- ter's scale, occupying half its length. It will be known b}r slanting lines which cross it at each end. The length of the scale, not occupied by these oblique lines, is equally divided into several larger divisions, numbered on one side, and like- wise twice as many smaller, numbered on the other. In ta- king distances from the scale, each of these divisions, (either the larger or the smaller, as is most convenient,] must be considered 1, 10, 100, &:c, rods, chains, or other dimensions of length. If each division be called 1, it will be easy to take off the required number. But the scale is not usually long enough for this. When each division is called 10, as many divisions must be taken, as there are tens in the given number. For the excess of tens, in this case, the little scale, with the oblique lines, is used. Each side of this little scale is divi- ded into 10 equal parts, and each of these parts is, of course, 1. Then, to take off the hypothenuse, 25, above, we should take in the dividers 2 of the divisions of the large scale, and 5 of those of this small one. There is one of these little scales for the greater, and one for the smaller divisions of the large scale. When each division of the large scale is called 10^ each of those of the small one becomes 10, and the units are found by means of the oblique lines. These are drawn across parallel lines, running the whole length of the scale, from each division on one side, to the next higher on 20 GEOMETRY. the other. The parallel lines divide the width of the scale into 10 equal parts. Since each oblique line, then, in cross- ing the scale passes over one division of length, it is ev- ident, that, in passing one tenth across, (that is, to the first parallel line,) it will pass over one tenth of a division of length ; in passing two tenths across (that is, to the second parallel line,) it will pass over two tenths of a division of length, and so on. The parallel lines are numbered at the end of the scale. To take off a distance, containing hun- dreds, then, as 234, we must place one foot of the dividers on the second division of the larger scale, and on the parallel line marked 4, and extend the other foot to the third oblique ine. Decimals may evidently be taken ofi in a similar man ner ; the divisions of the larger scale being made units, and those of the smaller, tenths and hundredths.] Note. The length of the two legs may be found by mea- suring them upon the same scale of equal parts from which the hypothenuse was taken. Fig. 31 PROBLEM X. To male a right an- gled triangle, the angles and one leg being given. Fig. SI. Suppose the angle at C 33° 15', and the leg AC 285. Draw the leg AC making it in length 285 ; at A erect a perpendicular an indefinite length ; at C make an angle of 33" 15' ; through where that number of degrees cuts the arc, draw a line till it meets the perpendicular at B. Note. If the given line CA should not be so long as the chord of 60°, it may be continued beyond A, for the purpose of making the angle. Fig. 32. PROBLEM XI. To male a right an- gled triangle, the hypothenuse and one leg being given. Fig. 32. Suppose the hypothenuse AC 40, and the leg AB 28. Draw the leg AB in length 28 ; from B erect a perpendic- GEOMETRY. 21 ular an indefinite length ; take 40 in the dividers, and setting one foot in A, wherever the other foot strikes the perpendic- ular will be the point C. Note. When the trianglo is constructed, the angles may be measured by a protractor, or by a scale of chords. Fig. 33. C PROBLEM XII. To make a right angled triangle, the two legs leing given. Fig. 33. Suppose the leg AB 38, and the leg BC 46. Draw the leg AB in length 38 ; from B erect a perpendic. ular to C in length 46 ; and draw a line from A to C. Fig, 34. PROBLEM XIII. To make an oblique angled tri- angle, the angles and one side being given. Fig, 34. Suppose the side BC 98 ; the angle at B 45 '^ 15', the angle at D 108° 30', consequently the other angle 26^ 15'. Draw the side BC in length 98 ; on the point B make an angle of 45° 15' ; on the point C make an angle of 26° 15', and draw the lines BD and CD. Fig, 35. PROBLEM XIV. To make an oblique angled triangle, two sides and an angle op- posite to one of them being given. Fig, 35. £eo i^C Suppose the side BC 160, the side BD 79, and the angle at C 29° 9'. Draw the side BC in length 160 ; at C make an angle of 29° 9', and draw an indefinite line through where the degrees cut the arc ; take 79 in the dividers, and with one foot in B lay the other on the line CD ; the point D will be the other angle of the triangle. C 22 GEOMETRY. Fig. 36. PROBLEM XV. To make an oh- » lique angled triangle, two sides and their contained angle being given. Fig. 36. B ^^^ Suppose the side BC 109, the side BD 76, and the angle atB 101° sa. Draw the side BC in length 109 ; at B make an angle of 101° 30', and draw the side BD in length 76 ; draw a line from D to C and it is done. Fig. 3" PROBLEM XVL To make a Square. Fig. 37. Draw the line AB the length of the proposed Square ; from B erect a perpendicular to C and make it of the same length as AB ; from A and C, whh the same distance in the dividers, describe arcs intersecting each other at D, and draw the lines AD and DC Fig. 38. PROBLEM XVII. gle. Fig. 38. To make a rectan- Draw the line AB equal to the longest side of the rec- tangle ; on B erect a perpendiculajr the length of the shortest side to C ; from C, with the longest side, and from A, with the shortest side, describe arcs intersecting each other at D, and draw the lines AD and CD. GEOMETRY. 33 Fig, 39. PROBLEM XVIII. To de- >^ scribe a circle which shall pass through any three given points^ not lying in a right line, as Ay B, D. Fig. 39. Draw lines from A to B and from B to D ; bisect those lines by problem II. and the point where the bisecting lines intersect each other, as at C, will be the centre of the circle. PROBLEM XIX. To find the centre of a circle. By the last problem it is plain, that if three points be any where taken in the given circle's periphery, the centre of the circle may be found as there taught. Directions for constructing irregular figures of four or more sides may be found in the following treatise on Surveying. TRIGONOIETRY. TRIGONOMETRY is that part of practical Geometry by which the sides and angles of triangles are measured : where- by three things being given, either all sides, or sides and an- gles, a fourth may be found ; either by measurioi^ with a scale aad dividers, according to the Problems i^- Geometry, or more accurately by calculation with logarithms, or with natu- ral sines. Tbigo^'o^ietey is divided into two parts, rectangular and oblique-aiDgular. PART I. RECTANGULAR TRIGONOMETRY. This is founded on the following methods of applying a circle to a triangle. Fig. 40. PROPOSITION I. In ever>- right angled triangle, as ABC, Fig. 40, it is plain from FiS' "», compared with the Geometrical definitions to which that Figure refers, that if the hypothenuse A AC be made radius, and with it an arc of a circle be described from each end, BC will be the sine of the angle at A, and AB the sine of the angle at C ; that is, the legs will be sines of their opposite angles. /%. 41. PROPOSITION II. If one leg, AB, Fig. 41, be made radius, and with it on the point A an arc be described, then BC, the other leg, will be the tangent, \ and AC the secant of the angle at A ; ' and if BC be made radius, and an arc be described with it on the point G, then AB will be the tangent and AC the se- A> cant of the angle at C ; that is, if one leg be made radius the other leg will be a tangent of its opposite angle, and the hypothenuse a secant of the same angle. c /\ \ / \ B TRIGONOMETRY. 25 Thus, as different sides are made radius, the other sides acquire different names, which are either sines, tangents or secants. As the sides and angles of triangles bear a certain propor- tion to each other, two sides and one angle, or one side and two angles being given, the other sides or angles may be found by instituting proportions, according to the following rules. Rule I. To find a side, either of the sides may be made radius, then institute the following proportion : As THE NAME OF THE SIDE GIVEN, (which will be eithci ra- dius, sine, tangent or secant ;) Is TO THE LENGTH OF THE SIDE GIVEN ; • So IS THE NAME OF THE SIDE REQUIRED, (which also wiU bc either radius, sine, tangent or secant;) To THE LENGTH OF THE SIDE REQUIRED. Rule II. To find an angle one of the given sides must be made radius, then institute the following proportion : As THE LENGTH OF THE GIVEN SIDE MADE RADIUS ; Is TO ITS NAME, (that is radius ;) So IS THE LENGTH OF THE OTHER GIVEN SIDE ; To ITS NAiviE, (which will be either sine, tangent or se- cant.) Having instituted the proportion, look for the correspond- ing logarithms, in the logarithms of numbers for the length of the sides ; and in the table of artificial sines, and tangents, and for the logarithmic sine, tangent or secant. ' Add TOGETHER THE LOGARITHMS OF THE SECOND AND THIRD TERMS, AND FROM THEIR SUM SUBTRACT THE LOGARITHM OF THE FIRST term: THE REMAINDER WILL BE THE LOGARITHM OP THE FOURTH TERM, WHICH SEEK IN THE TABLES, AND FIND ITS CORRESPONDING NUMBER, OR DEGREES AND MINUTES. See the introduction to the table of logarithms ; which should be attentively studied by the learner before he pro- ceeds any further. Note. The logarithm for radius is always 10, which is the logarithmic sine of 90°, and the logarithmic tangent of 45. The preceding propositions and rules being duly at- tended to, the solution of the following cases of Rectangular Trigonometry will be easy. C2 26 TRIGONOMETRY. CASE. I. Fig. 42. The angles and hypothenuse given to find the legs. Fig. 42. In the triangle ABC, given tlie hypothenuse AC 25 rods or chains : the angle at A 35" 30' : and consequently the angle at C 54- 30' : (See note Geom. Def, 39.) to find the legs. Making the hypothenuse radius, the proportions will be Tojind the leg AB, As radius - - 10.00'''000 : hyp. AC, 25 - 1.397940 : : sine ACB, 54° 30' 9.910686 11.308626 10.000000 leg AB,20.35 nearly 1.308626 Tojind the leg BC. As radius - - 10.000000 :hvp. AC. 25 - 1.397940 : : sine CAB, 35° 30' 9.763954 11.161894 10.000000 leg BC, 14.52 nearly 1.161894 Note, When the first term is radius, it may be subtracted by cancelling the first figure of the sum of the other two terms. 3Iaking the leg AB radius, the proportioi>s will be : TofindtheJeg XB. As secant CAB, 35° 30' : hyp. AC, 25 : : radius : leg AB, 20.35 To find the leg BC. As secant CAB, 35*5 30' hvp. AC, 25 : tangent, CAB, 35° 30 leg BC, 14.52 Making the leg BC radius, the proportions will be : Tofindtheleg AB. As secant ABC. 54° 30' hyp. AC, 25 : tangent ACB, 54^ 30' leg AB, 20.35 To find the leg BC. As secant CAB, 54^ 30' : hyp. AC, 25 : : radius : leg. BC, 14.52 The logarithms of the four last proportions being looked out. and added and subtracted according to the rule^ the result ^vill be found to be the same as in the two first proportions. [The learner should exercise himself, in this and the following rules in Trigono^ietey, in stating all the proportions which eanbe made, until he is able to do it with facility.] TRIGONOMETRY. 27 By natural sines. This CASE may be solved by natural sines,* according to the following proportions : As UNITY OR 1, IS TO THE LENGTH OF THE HYPOTHENUSE, so IS THE NATURAL SINE OF THE S^IALLEST ANGLE, TO THE LENGTH OF THE SHORTEST LEG. Or, SO IS THE NATURAL SINE OF THE LARGEST ANGLE, TO THE LENGTH OF THE LONG- EST LEG. Or, which is the same thing, multiply the natural sines OF THE two angles BY THE HYPOTHENUSE : THE PRODUCTS will be the length of the two legs. Example. Nat. sine of 35° 30' Nat. sine of 54^ 30'. 0.58070 0.81412 Hyp. 25 Hyp. 25 290350 407060 116140 162824 14.51750 20.35300 Leg BC 14.52 Leg AB 20.35 Note. The third decimal figure in the first product being 7, the preceding figure may be called one more than it is, viz. 2, And whenever in any product, &c. there are more places of decimals than you wish to work with, if the one at the right hand of the last which you wish to retain is more than 5, add a unit to the last, because a greater decimal number than 5 is more than half. CASE H. Fig, 43. C The angles and one leg given to find the hypothenuse and the.gther leg. Fig. 43. In the triangle ABC, given the leg AB 325, the angle at A 33° 1-5' and the angle at C 56° 45' : to find the hypothenuse and the leg BC. * See the Introduction to the Table of Natural Sines. 28 TRIGONOMETRY. Making the given leg radius, the proportions will be To find the hypothenuse. As radius, 10.000000 : leg AB. 32.5 2.511883 10.077645 ; : sec. CAB. SS'^ 15' ; hyp. 388.6 12.589528 To find the leg BC. As radius, lO.GOOOOO : leg AB, 325 2.511883 : : tan. CAB, 33^ 15' 9.816653 : leg BC, 213.1 12.328541 Note. Reject the first figure, which is the same as subtract- ing radius, and seek the numbers corresponding to the other figures. Making the leg BC radius, the proportions will be : Tofnd the hypothemise. As taug. ACB, 5G^ 45' les AB, 325 : sec. ACB, 56^ 45 h}i). 388.6 Making the hypothenuse radius, the proportions will be ; Tofnd the le^ BC. As tang. ACB, 56= 45' : leg AB, 325 : : radius : lea BC, 213.1 To find the hypothenuse. As sine BCA, 56= 45' : leg AB, 325 : : radius : hyp. 38S.G To find the leg BC. As sine BCA, 56= 45' : le^ AB. 325 : : sme BAG. 33° 15' : le^BC, 213.1 Note. If the leg BC had been given, instead of the leg AB, the proportioBs would have been the same, the obvious chano-es bein^ made. Br ^■AT^EAL SIXE; To solve this case by natural sines, institute the following proportions : To find the hypothenuse. As the ^-AT^RAL si>:e of thb AIS'GLE OPPOSITE THE' GIVEN LEG, IS TO THE LE>"GTH OF THE LEG, SO IS r:^"ITT OR 1, TO THE LE^•GT^ OF THE HYPOTHE- rsTSE. Or which is the same thing, divide the give>' leg by THE ^-AT^RAL SINE OF ITS OPPOSITE AXGLE, AND THE QITO- TIETfT W ILL BE THE HYPOTHENTSE. * Find the sec. as directed in the introduction to the tables, bj sub- tracting the co-sine from 20.000.000.— Ed. TRIGONOMETRY. 29 To find the other leg. As the natural sine of the an- gle OPPOSITE THE GIVEN LEG, IS TO THE LENGTH OF THE GIV- en leg, 60 is the natural sine of the angle oppositb the other leg, to the length of the other leg. Example. Given leg 325. Nat. sine of 56<^ 45', the angle opposite the given leg 0.83629. Nat. sine of 33° 15', the angle op- posite the other leg 0.54829. As 0.83629 : 325 : : 1 : 388.6. As 0.83629 : 325 : : 0.54829 : 213.07. CASE III. Fig. 44. The hypotlienuse and one leg given to find tJie angles and the other leg. Fig. 44. In the triangle ABC, given the hypothenuse AC 50 and the leg AB 40, to find the angles and leg BC. Making the hypothenuse radius, the proportion to find the angle ACB will be : As hyp. 50 : radius : : leg AB, 40 : sine ACB, 53° 8' 1.698970 10.000000 1.602060 11.602060 1.698970 9.903090 The angle ACB being 53° 8' the other is consequently 36° 52'. Making the leg AB radius, the angle BAG may be found ^ TRIGOXOMETRY. by the following proportion ; As leg AB, 40 ■ 1.602060 : radius - 10.000000 ; :h)-p. 50 . 1.698970 11.698970 1.60-2060 : sec. BAG, 36" 52 10.096910 The angles being found, the leg BC may be found by ei- ther of the preceding cases. It is 30. By ^'ATnlAL sixes. The angle opposite the given leg may be found bv the fol- lowing proportion ; As THE HYPOTHENUSE IS TO UNITY OR 1, SO IS THE GIVEN LEG TO THE NAT. SINE OF ITS OPPOSITE ANGLE. Or, which is the same thing, divide the given leg by the HrPOTHENUSE, AND THE QUOTIENT WILL BE THE NAT. SINE. Example. The leg AB 40 divided by the hypothenuse 50 gives a quo- tient 0.80000 which looked in the table of nat. sines, the near- est corresponding number of desrrees and minutes will be found to be 53= 8, the angle ACBT By the square root. In this CASE the required leg may be found by the squsire root, without finding the angles ; according to the following PROPOSITION ; In every RIGHT ANGLED TRIANGLE, THE SQUARE OF THE HYPOTHENTTSE IS EQUAL TO THE SUM OF THE SQUARES OF THU TWO LEGS. Hence, The square of the given leg being subtracted from TRIGONOMETRY. 31 THE SQUARE OF THE HYPOTHENUSE, THE REMAINDER WILL BE THE SQUARE OF THE REQUIRED LEG* As in the preceding example ; the square of the leg AB 40 is 1600 ; this subtracted from the square of the hypothe- nuse 50 which is 2500, leaves 900, the square of the leg BC, the square root of which is 30, the length of leg BC as found by logarithms. CASE IV. The legs given to find the angles and hy- pothenuse. Fig. 45. 7^,r In the triangle ABC, given the leg AB 78.7 and the leg BC 89 ; to find the angles and hypothenuse. Making the leg AB radius, the proportion to find the angle BAC will be ; Asleg AB, 78.7 1.895975 : radius - - 10.000000 : : leg BC, 89 - 1.949390 11.949390 1.895975 tang. BAC, 48° 31' 10.053415 The angle ACB is consequently 41° 29'. Making the leg BC radius, the proportion to find the angle BCA will be similar, with the obvious differences. The angles being found, the hypothenuse may be found by Case II. It is nearest 119. 32 TRIGONOMETRY. By the square root. In this case the hypothenuse may be found bv the square root, without finding the angles ; according to the following PROPOSITIO^^ In every right angled triangle, the SU3I OP THE SQUARES OF THE TWO LEGS IS EQUAL TO THE SQUARE OP THE HYPOTHENUSE. In the above example, the square of AB 78.7 is 6193.69, the square of BC 89 is 7921 ; these added make 14114.69 the square root of which is nearest 119. By natural sines. The hypothenuse being found by the square root, the angles mav be found by nat. sines, according to the preceding case. Hvp. Leg. BC. Nat. Sine. liQ) 89.00000 (74789 83 3 570 The nearest degrees and minutes 476 corresponding to the above nat. sine are 48° 24', for the angle BAC. The 940 difference between this and the angle 833 as found by logarithms is occasioned by dividing by 119, which is not the 1070 exact length of the hypothenuse, it 952 being a fraction too much. 1180 1071 109 PART II. Oblique trigonometry. The solution of the first two cases of Oblique Trigonome- try depends on the following proposition. In all plane triangles, the sides are in proportion TO EACH other AS THE SINES OF TUEIE OPPOSITE ANGLES. TRIGONOMETRY. 33 That is, as the sine of one angle is to its opposite side, so is the sine op another angle to its opposite side. Or, as one side is to the sine of its opposite angle, so is another side to the sine of its opposite angle. [Note. When an angle exceeds 90° make use of its supple- ment, which is what it wants of 180°. Note Def, 26. Geom.] CASE I. The angles and one side given to find the other sides. Fig, 46. 2aa In the triangle ABC, given the angle at B 48°, the angle at C 72°, consequently the angle at A 60°, and the side AB 200, to find the sides AC and BC. To Jin d the side AC. As sine ACB, 72° - 9.978206 : side AB, 200 - 2.301030 : : sine ABC, 48° - 9.871073 : side AC, 156 12.172103 9.978206 2.193897 Tojind the side BC. As sine ACB, 72° - 9.978206 : side AB, 200 - 2.301030 : : sine BAC, 60** - 9.937531 side BC, ia2 12.328561 9.978206 2.260355 By natural sines. As the NAT. sine OF THE ANGLE OPPOSITE THE GIVEN SIDE IS TO THE GIVEN SIDE, SO IS THE NAT. SINE OF THE ANGLE OP- POSITE EITHER OP THE REQUIRED SIDES TO THAT REQUIRED SIDE. Given side 200 ; nat. sine of 72°, its opposite angle, 0.95115; nat. sine of ABC 48°, 0.74334; nat. sine of BAC 60° 0.86617. Thus, D 34 TRIGONOMETRY. 0.95115 : 200 : : 0.74334 : 156 0.95115 : 200 : : 0.86G17 : 182. CASE II. Two sides, and an angle opposite to one of them given, to find the other angles and side. Fig, 47. Z4t? In the triangle ABC, given the side AB 240, the side BC 200, and the angle at A 46'' 30' ; to find the other angles and the side AC. Tojind the angle ACB. As side BC, 200 2.301030 : sine BAC, 46= 30' 9.860362 :: side AB, 240 2.38U211 12.240773 2.301030 rsineACB, 60° 30' nearly 9.939743 Angle at A C 46° 30' 60 30 107.00 Sum of the three angles Sum of two 180° 107 Angle at B The side AC will be found by case I. to be nearest 253. Note. If the given angle be obtuse, the angle sought will be acute ; but if the given angle be acute, and opposite a given lesser side, then the angle found by the operation maybe either obtuse or acute. It ought therefore to be mentioned which it is, by the conditions of the question. By natural sines. As THE SIDE OPPOSITE THE GIVEN ANGLE IS TO THE NAT. SINE OF THAT ANGLE, SO IS THE OTHER GIVEN SIDE TO THE NAT. SINE OF ITS OPPOSITE ANGLE. One given side 200, nat. sine of 46° 30', its opposite angle, 0.72537, the other given side 240. As 200 ; 0.72537 : : 240 : 8.87044=60° 30'. TRIGONOMETRY. CASE III. Two sides and their contained angle giv- en, to find the other angles and side. Fig, 48. Fig. 48. 240 The solution of this case depends on the following proposi- TIOX. In every plane triangle, as the sum of any two' sides IS TO their difference, so is the tangent of half the SUM of the two opposite angles to the tangent of half THE difference BETWEEN THEM. Add THIS half difference to half the sum of the an- gles AND you will have THE GREATER ANGLE, AND SUBTRACT THfi HALF DIFFERENCE FROM THE HALF SUM AND YOU WILL have THE LESSER ANGLE. In the triangle ABC, given the side AB 240, the side AC 180, and the angle at A 36^ 40' to find the other angles and side. SideAB - 240 AB - 240 AC . 180 AC - * 180 Sum of the two sides 420 Difference 60 The given angle BAC 36° 40', subtracted from 180°, leaves 143° 20' the sum of the other two angles, the half of which is 71° 40'. As the sum of two sides, 420 - - 2.623249 : their difference 60 . - - 1.778151 : : tangent half unknown ang. 71° 40' 10.479695 : tangent half difference, 23° 20' nearly The half sum of the two unknown angles, The half difference between them, Add, gives the greater angle ACB Subtract, gives the lesser angle ABC The side BC may be found by case I or II, 12.257846 2.623249 9.634597 71° 40' 23 20 95 00 48 23 36 TRIGONOMETRY. CASE IV. The three sides given to find the an- gles. Fig. 49. The solution of this case depends on the following propo- SITION. In every plane triangle, as the longest side is TO THE SUM OF THE OTHER TWO SIDES, SO IS THE DIFFERENCE between THOSE TWO SIDES TO THE DIFFERENCE BETWEEN THE SEGMENTS OF THE LONGEST SIDE, MADE BY A PERPENDIC- ULAR LET FALL FROM THE ANGLE OPPOSITE THAT SIDE. Half the difference between these segments, added to half the sum of the segments, that is, to half the length of the longest side, will give the greatest segment ; and this half xiif- ference subtracted from the half sum will be the lesser seg- ment. The triangle being thus divided, becomes two right angled triangles, in which the hypothenuse and one leg are given to find the angles. In the triangle ABC, given the side AB 105, the side AC 85, and the side BC 50, to find the angles. Side AC - 85 AC - - 85 BC - 50 BC - - 50 Sum of the two sides 135 Difference As the longestiside AB, 105 : sum of the other two sides, 135 : difference between those sides, 35 : difference between the segments, 45. Half the side AB Half the difference of the segments Add, gives the greater segment AD Subtract, gives the lesser segment BD 35 2.021189 2.130334 1.544068 3.674402 2.021189 1.653213 TRIGONOMETRY, 37 Thus the triangle is divided into two right angled trian- gles, ADC and BDC ; in each of which the hypothenuse and one leg are given to find the angles. Tojind the angle DCA. To find the angle DCB Ashyp. AC, 85 - 1.929419 " ' -- : radius - - 10.000000 : : seg. AD, 75 - 1.875061 sine DCA, Gl*' 56' 1I.875G61 1.929419 9.945642 As hyp. BC, 50 - 1,698970 : radius 10.000000 : : seg. BD, 30 1.477121 11.477121 1.698970 sine DCB, 36° 52' 9.778151 The angle DCA 61^ 56' subtracted from 90° leaves the angle CAD 28° 4'. The angle DCB 36° 52' subtracted from 90^ leaves the an- gle CBD 53° 16'. The angle DCA 61° 56' added to the angle DCB 36° 52 gives the angle ACB 98° 48'. This CASE may also be solved according to the following PROPOSITIOX. In every plane triangle, as the product OF ANY TWO SIDES CONTAINING A REQUIRED ANGLE IS TO THE PRODUCT OF HALF THE SUM OF THE THREE SIDES, AND TflE D1PPERB^CE BETWEEN THAT HALF SUM AND THE SIDE OPPOSITE THE ANGLE REQUIRED, SO IS THE SQUARE OF RADIUS TO THE SQUARE OF THE CO'SINE OF HALF THE ANGLE REQUIRED. Those who make themselves well acquainted with trigo- ^"OMETRY will find its application easy to many useful purpos- es, particularly to the mensuration of heights and distances ; These are here omitted, because, as this work is designed principally to teach the art of common field-surveying, it was thought improper to swell its size, and consequently in=. crease its price, by inserting any thing not particularly con- nected w^ith that art. It is recommended to those who design to be surveyors to study TRIGONOMETRY thoroughly ; for though a common field may be measured without an acquaintance with that science, yet many cases will occur in practice where a knowledge of it will be found very beneficial ; particularly in dividing land, and ascertaining the boundaries of old surveys. Indeed no one who is ignorant of trigonometry, can be an accom- plished surveyor. D2 SURVEYING. SURVEYING is the art of measuring, laying out, and di- viding land. PART I. Measuring land. The most common measure for land is the acre ; which contains 160 square rods, poles or perches ; or 4 square roods, each containing 40 square rods. The instrument most in use, for measuring the sides of fields, is Gunter's chain, which is in length 4 rods or 66 feet ; and is divided into 100 equal parts, called links, each containing 7 inches and 92 hundredths. Consequently, 1 square chain contains 16 square rods, and 10 square chains make 1 acre. In small fields, or where the land is uneven, as is the case with a great part of the land in New England, it is better to use a chain of only two rods in length ; as the survey can be more accurately taken. SECTION I. Preliminary problems. PROBLEM I. To reduce two rod chains to four rod chains. Rule. If the number of two rod chains be even, take half the number for four rod chains, and annex the links if any ; thus, 16 two rod chains and 37 links make 8 four rod chains and 37 links. But if the. number of chains be odd, take half the greatest even number for chains, and for the remaining number add 50 to the links : Thus, 17 two rod chains and 42 links make 8 four rod chains and 92 links. PROBLEM II. To reduce two rod chains to rods and de- emed parts. SURVEYING. 39 Rule. Multiply the chains by 2, and the links by 4, which will give hundredths of a rod ; thus, 17 two rod chains and 21 links make 34 rods and 84 hundredths ; expressed thus, 34.84 rods. If the links exceed 25, add 1 to the number of rods and multiply the excess by 4 : thus, 15 two rod chahis and 38 links make 31.52 rods. PROBLEM III. To reduce four rod chains to rods and decimal parts. Rule. Multiply the chains, or chains and links, by 4 ; the product will be rods and hundredths : thus, 8 chains and 64 links make 34.56 rods. Note. The reverse of this rule, that is, dividing by 4, will reduce rods and decimals to chains and links : thus, 105. 12 rods make 26 chains and 28 links. PROBLEM IV. To reduce square rods to acres. Rule. Divide the rods by 160, and the remainder by 40, if it exceeds that number, for roods or quarters of an acre : thus 746 square rods make 4 acres, 2 roods, and 26 rods. PROBLEM V. To reduce square chains to acres Rule. Divide by 10 ; or, which is the same thing, cut off the right hand figure ; thus, 1460 square chains make 146 acres ; and 846 square chains make 84 acres and 6 tenths. PROBLEM VI. To reduce square links to acres. Rule. Divide by 100000 ; or, which is the same, thing, cut off the 5 right-hand figures : thus, 3845120 square links make 38 acres and 45120 decimals. Note. "When the area of a field, by which is meant its superficial contents, is expressed in square chains and links, the whole may be considered as square links, and the number of acres contained in the field, found as above. Then multiply the figures cut olFby 4, and again cut ofFS figures, and you have the roods ; multiply the figures last cut off by 40, and again cut off 5 figures, and you have the rods. Example. How many acres, roods, and rods, are there in 156 square chains and 3274 square links ? 15)63274 square links, 4 2)53096 40 21)23840 Anstoer. 15 acres 2 roods and 21 rods. 'PROBLEMsforJinding the area oj righf lined figures, and aha of circles. 40 SURVEYING. PROBLEM VII. To find the area of a square or rectati' gle. Rule. Multiply the length into the breadth ; the product will be the area. PROBLEM VIII. To find the area of a rhombus or rhomboid. Rule. Drop a perpendicular from one of the angles to its opposite side, and multiply that side into the perpendicular ; the product will be the area. PROBLEM IX. To find the area of a triangle. Rule 1. Drop a perpendicular from one of the angles to its opposite side, which may be called the base ; then multi- ply the base by half the perpendicular; or the perpendicular by half the base ; the product will be the area. Or, multiply the whole base by the whole perpendicular, and half the pro- duct will be the area. Rule 2. If it be a right angled triangle, multiply one of the legs into half the other ; the product will be the area. Or, multiply the two legs into each other, and half the pro- duct will be the area. Rule 3. When the three sides of a triangle are known, the area may be found arithmetically, as follows : Add together the three sides ; from half their sum subtract each side, noting down the remainders ; multiply the half sum by one of those remainders, and that product by another remainder, and that product by the other remainder ; the square root of the last product will the area.* Example. Suppose a triangle whose three sides are 24, 20, and 18 chains. Demanded the area. 24x20x18=62, the sum of the three sides, the half of which is 81. From 31 subtract 24, 20, and 18 ; the three remainders will be 7, 11, and 13. 31x7=217; 217x11=2387; 2387x13=31031, the square root of which is 176.1, or 17 acres 2 roods and 17 rods. By logarithms. As the addition of logarithms is the same as the multiplica- tion of their corresponding numbers ; and as the number an- swering to one half of a logarithm will be the square root of the number corresponding to that logarithm : it follows, that if the logarithm of the half sum of the three sides and the log- arithms of the three remainders be added together, the num. * Better expressed thSft. From half the sum of the sides subtract each side separately. Multiply the half sum and the several remainders together, and the square root of the product will be the area. — Ed . SURVEYING. 41 ber corresponding to one half the sum of those logarithms will be the area of the triangle. The half sum, 31 - - - 1.491362 The first remainder, 7 - - - 0.845093 The second remainder, 11 - - 1.041393 The third remainder, 13 - - 1.1 13943 The square of the area, 31030.083 nearly Area 176 square chains 150 square links 4.491796 2.245893 Rule 4. When two sides of a triangle and their contained angle, that is, the angle made by those sides, are given, the area may be found as follows : Add together the logarithms of the two sides and the lo- garithmic sine of the angle ; from their sum subtract the lo- garithm of radius, the remainder will be the logarithm of double the area. Example. Suppose a triangle one of whose sides is 105 rods and another 85, and the angle contained between them 28^ 5'. Demanded the area. One side, 105 - - - 2.021189 The other side, 85 - - - 1.929419 Sine angle, 28° 5' - - - 9.672795 13.623403 10.000000 3.623403 Subtract radius Double area, 4200 rods nearly Answer. 2100 rods. Note. Radius may be subtracted by cancelling the left-hand figure of the index, or subtracting 10, without the trouble of setting down the ciphers. By natural sines. Multiply the two given sides into each other, and that pro- duct by the natural sine of the given angle ; the last product will be double the area of the triangle. Nat. sine of the angle 28° 5' 0.47076. 105x85= 8925, and 8925x0.47076=4201 the double area of the triangle. PROBLEM X. To find the area of a trapezoid. 43 SURVEYING. Rule. Multiply half the sum of the two parallel sides by the perpendicular distance between them, or the sum of the two parallel sides by half the perpendicular distance, the pro- duct will be the area. PROBLEM XI. To find the area of a trapezium, or irreg- ular Jour sided figure . Rule. Draw a diagonal between two opposite angles, which will divide the trapezium into two triangles. Find the area of each triangle and add them together. Or, multiply the diagonal by half the sum of the two perpendiculars let fall upon it, or the sum of the two perpendiculars by half the di- agonal, the product will be the area. Note. Where the length of the four sides and of the diagonal is known, the area of the two triangles, into which the trapezium is di- vided, may be calculated arithmetically, according to Prob. IX. Rule 3. PROBLEM XII. To find the area of a figure containing more than four sides. Rule. Divide the figure into triangles, and trapezia, by drawing as many diagonals as are necessary, which diagonals must be so drawn as not to intersect each other ; then find the area of each of the several triangles or trapezia, and add them together ; the sum will be the area of the whole figure. Note. A little practice will suggest the most convenient way of draw- ing the diagonals ; but whichever way they are drawn, provided they do not intersect each other, the whole area will be found the same. PROBLEM XIII. Respecting circles. Rule 1. If the diameter be given the circumference may be found by one of the following proportions : as 7 is to 22, or more exactly, as 113 is to 355, or in decimals, as 1 is to 3.14159, so is the diameter to the circumference. Rule 2. If the circumference be given the diameter may be found by one of the following proportions : as 22 is to 7, or as 355 is to 113, or as 1 is to 0.31831, so is the circumfer- ence to the diameter. Rule 3. The diameter and circumference being known, multiply half the one into half the other, and the product will be the area. Rule 4. From the diameter only, to find the area : multi- ply the square of the diameter by 0.7854, and the product will be the area. Rule 5. From the circumference only to find the area \ SURVEYING. 48 multiply the square of the circumference by 0.07958, and the product will be tl^OTca. Rule 6. The area being given to find the diameter : divide the area by 0.7854, and the quotient will be the square of the diameter ; from this extract the square root, and you will have the diameter. Rule 7. The area being given to find the circumference : divide the area by 0.07958, and the quotient will be the square of the circumference ; from this extract the square root, and you will have the circumference. SECTION II. The following cases teach the most usual methods of taking the survey of fields ; also, how to protract or draw a plot of them, and to calculate their area. Note. Thejield-book is a register containing the length of the sides, of a field, as found by measuring them with a chain ; also the bearings or courses of the sides, or the quantity of the several an- gles, as found by a compass or other instrument for that purpose ; together with such remarks as the surveyor thinks proper to make in the field. CASE I. To SURVEY A TRIA?fGULAR FIELD. Measure the sides of the field with a chain, and enter their several lengths in a field book, protract the field on paper, and then find the area by prob. IX. Rule 1 . Or, without plot- ting the field, calculate the area by prob. IX. rule 3. Fig, 50. FIELD BOOK. See Fig. 50. c Chains. AB - - 20 BC - - 24 CA . - 18 To find the area, Ch. L. Base BC - - 24.00 Halfperp.AD - 7.34 ^ ^^ ^^ 9600 44 SURVEYL\G. 9600 7200 16S00 Acres 17)61600 4 Roods -2 )46400 40 Rods 18)56000 Acres Roods Rods Area 17 — 2 — 18.56 Note. When there are ciphers at the riorht hand of the liiiks, they mar be rejected : remembering to cut o5" a proper number of fig- ures according to decimal rules. Obserre, That in measuring with a chain, slant or incUned surfaces, as the sides of hills, should be measured horizontally, and not on the plane or surface of the hill : otherwise, a sur- vey cannot be accurately taken. To ecect this, the lower end of the chain must be raised from the ground, so as to have the whole in a horizontal line : and the end thus raised must be directly over the point w^here the chain begins or ends, ac* cording as you are ascending or descending a hill ; which point may be ascertained by a plummet and line. CASE U. To SrPvVEY A FIELD IX THE F0B3r OF A TEAPEZirX. Measure the several sides, and a diasfonal betv\-een two op. posiie angles ; protract the field, and find the area bv prob- LEM XI. Or, without protracting the field, calculate the area according to the note at the end of that PEOBLEir* Fi^. 51. FIELD BOOK. AB BC CD DA 0^^--^C . 72. ^ ^^_. SURVEYING. 45 To PROTRACT THIS TRAPEZtUM. Draw the side AB the given length ; with the diagonal AC 28 and the side BC 11.70 describe cross arcs as at C, from A and B as centres ; and the point of intersection will repre- sent that corner of the field : then, with the side CD 21.50 and the side AD 14.70, describe cross ares as at D, from A and C as centres ; and the point of intersection will represent that corner of the field. To FIND THE AREA. Perpendicular B a — Dm 11.34 11.10 Half diagonal AC 22.44 14.00 897600 2244 Acres 31)416 4 Rood 1)664 40 Rods 26)560 Acres Rood Rods Area 31 — 1 — 26.56 Note. The perpendiculars need not be actually drawn ; their length may be obtained as follows : From the angle opposite the diagonal open the dividers so as when one foot is in the angular point, as at B, the other, being moved backwards and forwards, may just touch the diagonal at A, and neither go the least above or below it ; that distance in the dividers being measured on the scale will give the length of the perpendicular. CASE III. To SURVEY A FIELD WHICH HAS MORE THAN FOUR SIDES, BY THE CHAIN ONLY. Measure the several sides, and from some one of the angles from which the others may be seen, measure diagonals to 46 SURVEYING. them ; draw a plot of the field, and find the area by prob- lem XII. FIELD BOOK. See Fig, 52. Fig, 52 30 fiO Ch.L. AB 30.60 BC 20.40 CD 22.40 AC DE 16.20 AC EF 13.50 AE FA 28. Diagonals, Ch.L. 45. 35. 24.20. To PROTRACT THIS FIELD. Draw the side AB, making it the given length 30.60 ; with the diagonal AC 45 and the side BC 20.40, describe cross arcs as at C, from the points A and B as centres, and the point of intersection will represent that corner of the field ; draw the side BC and the dotted diagonal AC ; with the dia gonal AD 35 and the side CD 22.40, describe cross arcs as at D, from the Points A and C, and draw the Side CD and the dotted diagonal AD. Proceed in this manner till all the sides and diagonals are drawn. To FIND THE AREA. Tne field being plotted, may be divided into one trapezium and two triangles ; the area of which is calcu ated as fol- lows : — SURVEYING. 47 The trapezium ABCD. Perpend. B a — Do Halfdiag.AC Square chains 11.68 17.10 27.78 22.50 143900 5756 5756 647.5500 The triangle AFE. Perpend. En - - 11.65 Half side AF - - 14 Square chains Acres Roods Rods Area 98 — — 34.4 4660 1165 163.10 The triangle ADE. Half perp. Em Diag. AD - - - Square chains 4.90 35 2450 1470 171.50 Trap. ABCD Triangle ADE Triangle AFE - 647.55 - 171.50 - 163.10 Acres 98)215 4 Roods .860 40 Rods 34)400 REMARKS. As each of the sides of the several triangles, into which the preceding plot of a field is divided, is known from the field book, the area of the field may be calculated arithmetically, by finding the area of each triangle, according to prob. IX. Rule 3 ; and then adding the whole together. This method, though it may require more time, is preferable to the other, because more accurate. Indeed it is always better to calcu- late the area of a field arithmetically than geometrically ; for in the former no two persons can differ in their calcula- tions ; whereas, according to the latter, which is the com- mon method of casting the contencs of a field, it is hardly to be expected that any two persons will perfectly agree. The inaccuracy of scales, and the difficulty of determining with precision the length of sides and perpendiculars with a scale and dividers, render it almost if not quite impossible to obtain the exact area of a field, in the method commonly practised, even if the surveyor has measured it accurately in the first place. Other methods of taking the survey of a field by the chain only are mentioned in some treatises on this subject, but they 48 SURVEYING. are rather curious than useful ; and it is much better to ascer- tain the asgles by an accurate compass, or some instrument designed purposely for taking angles. CASE IV. To SURVEY A FIELD WITH A CHAIX A>'D COMPASS. Measure the length of the sides with a chain, and take their bearing or course with a compass ;* enter these in a field book ; plot the field on paper, and calculate the area by the directions already given. To PROTRACT OR DRAW A MAP OF A FIELD. Draw a line to represent a meridian, or north and south line, from which lay off a bearing or course of the first side of the field, with a protractor or from a line of chords ; and from a scale of equal parts, measure the length of the side and draw a line to represent it. At the end of this line draw a line parallel to the meridian line, and then lay off the second side of the field as before taught ; proceed in the same manner to draw parallel lines, and lay off the several sides till the whole is protracted. In protracting a field, let the top of the paper be considered as north, the bottom south, the right hand east, and the left hand west ; lay the course to the right or left of the meridian line, according as it is east or west, and upwards or down- wards, according as it is north or south. In all protractions, if the end of the last distance falls ex- actly on the point from which you began, the course also be- ing right, the field work and protractions are truly taken and performed ; if not, an error must have been committed in one of them : in such cases, make a second protraction ; if this agrees with the former, it is to be presumed the fault is in the field work ; a re-survey must then be taken. * A compass may be so constructed with two indexes, one moveable and the other fixed, as to ascertain the angle made by two sides, without reference to the bearing of those sides. Such a compass would be par- ticularly usefiil in surveying land where there are mineral substances which have an influence upon the compass needle, attracting it one way w the other, and thus rendering it impossible to take a course by ii with precision. SURVEYING FIELD BOOK. See Fig. 53. Ch. L. f 1 AB. N. 7° 0' W. 28.20 BC. N. 74 E. 39.50 »^ CD. S. 9 E. 38. i\ i \ DE. N. 63 20 W. 14.55 \ EA. S. 74 W. 28.60 ill Acres Rood Rods 1 \i Area 117 — 1 ■ -6 iaP REMARKS. 49 Fig. 53. The sides of the several triangles into which the plot of a field is divided may be found by trigonometry ; and then the area of each triangle may be calculated according to pros. IX. Rule 3. The sum of the areas of the several triangles will be the area of the whole field. This method may re- quire more time, but it is perfectly accurate, since no de- pendence is placed on the uncertain measurement of scale and dividers.* In the preceding example, suppose the field divided into three triangles. See Fig. 53. In the triangle E\B, the sides EA and AB are known from the field book, and their contained angle is known from the bearing of the sides. The other angles and the side EB may be found by oblique trig- o^'OMETRY, CASE III. ; and then there will be the three sides to find the area. In the triangle EBC, the side BC is known from the field book, and the side EB is found as above men- tioned ; the angle EBA is also found as above ; this subtract- ed from the angle ABC, which may be found from the bear- ing of the sides AB and BC, will leave the angle EBC : there will then be the two sides and their contained angle to find the third side ; and this being found, there will be the three sides to find the area. In the triangle EDC, the sides DE and DC are known from the field book, and their contained angle is known from the bearing of the sides. The side EC and the area may be found as above. It is recommended to the learner to make these calcula- * As accuracy is of much higher importance than expedition, no practical surveyor should ever depend upon his scale and dividers. — Ed. E2 50 SURVEYING. tions, as it will improve him in the knowledge of trigonome- try. Note. Two sides and their contained angle being given, the area may be found by prob. IX. Rule 4. Another method of protracting fields. Without drawing parallel lines at the end of each side, a field may be protracted by the angles made by the several sides ; and the angle made between any two sides may be found by the following rules. Rule 1, If the course or bearing of one of the sides is north and the other south, one east and the other west, sub- tract the less course from the greater. Rule 2. If one is north and the other south, and both east or west, add both courses together. Rule 3. If both are north or south, and one east and the other west, subtract their sum from 180^. Rule 4. If both are north or south, and both east or west, add the less course, and the supplement of the greater. In each case, the result will give the angle contained by the two sides. To protract a field according to the preceding rules is pre- ferable to the method of doing it by parallel lines, though it may not be so easy to the learner at first. It is difficult to draw parallel lines with perfect accuracy, and a small devia- tion from a true line may make considerable difference in the plot of a field. Example II. FIELD BOOK. See Fig. 54. Ch.L. AB. N. 16O30' E. 22. BC. N. 82 E. 19.60 CD. S. 17 E. 24. DE. S. 37 W. 22. EA. N. 49 W. 25.20 Area 85 aeres. SURVEYING. 51 To DRAW A PLOT OF THIS FIELD, ACCORDING TO THE PRE- CEDING RULES. Having drawn the side AB, according to the directions be- fore given for laying off the first course and distance, com- pare the first and second courses together, and they will be found to be both north and both east ; consequently, the angle between them is found by rule 4, as follows : 16"^ 30' the less course, and 98° the supplement of the greater being added, the sum is 114° 30', for the angle at B. Compare the second and third courses, and they will be found to be one north and one south, and both east ; consequently, according to rule 2, 82° the second course added to 17° the third course, the sum 99° is the angle at C. The third and fourth courses are both south, and one east and the other west. The angle between them at D is 126° ; for 17° the third course added to 37° the fourth course is 54^, which subft-acted from 180° leaves 126», according to rule 3. The fourth and fifth courses are one south and the other north, and both west. According to rule 2, 37*^ the fourth course added to 49° the fifth course, the sum 86° is the angle at E. A little practice will render this mode of protracting a field familiar and easy, and an attention to the courses will show in what direction the angle is to be made. Example III. FIELD BOOK. See Fis. 59. 52 SURVEYING. Ch. L. AB. N. 56° 15' E. 21.60 BC. N. 26 30 E. 13.44 CD. S. 71 30 E. 18.96 DE. S. 26 30 E. 13.44 EF. S. 71 30 W. 18.96 FG. S. 45 E. 8.47 GH. s. 63 30 E. 13.44 HI. N. 45 E. 8.47 IK. S. 26 30 E. 13.44 KL. s. 45 W. 8.47 LM. s. 63 30 W. 13.44 MN. N. 76 W. 24.73 NA. N. 36 45 W. 30. Acres Rood ] Rods Area 167 — L — 30 The above field may be protracted, and its area calculated according to the directions given in the preceding examples. SeVEEAL field books to exercise the learner I?f PLOT- TING FIELDS AND CALCULATING THEIR AREA. No. 1, Rods. 1. N. 15° E. 320 2. N. 37 30. E. 160 3. East 120 4. S. 11 E. 200 5. South 216 6. West 160 7. S. 36 30 W. 160 8. N. 38 15 W. 136 Acres Roods Rods Area 744: — S — 28 No. II. Ch. L. 1. N. 75° 0' E. 13.70 2. N. 20 30 E. 10.30 3. East 16.20 4. S. 33 30 W. 35.30 5. S. 76 W. 16. 6. North 9. 7. S. 84 W. 11.60 Ch. L. 8. N. 53M5' W. 11.60 9. N. 36 45 E. 19.20 10. N. 22 30 E. 14. 11. S. 76 45 E. 12. 12. S. 15 W. 10.85 13. S. 16 45 W. 10.12 Acres Roods Rods. Area 110 — 2—23 No. III. Rods. 65°40' W. 49.7 67 15 W. 34.5 W. 17.9 W. 5.8 30 E. 29.4 E. 107.4 50 W. 22. 18 30 W. 46. Acres Rood Rods. Area 34—1 — 19 S. S. s. s. s. N. N. N. 54 20 83 5 SURV EYI P^G. 53 No. IV Rods. Rods. 1. N. 43° W. 12.44 16. N. 18^30' W. 39. 2. N. 64 w. 8. 17. N. 86 5 E. 26.7 3. N. 52 w. 14.60 Acres Rood Rods 4. N. 37 5 w. 51.36 Area 48 — 1 — 13 5. N. 15 30 w. 21.76 6. N. 20 40 w. 44.60 No. VII. Ch. L. 7. N. 88 20 E. 167.60 1. N. 0°45' W. 9. 8. S. 34 40 E. 71.20 2. N. 19 30 W. 5.35 9. s. 75 W. 69.72 3. N. 23 W. 4.09 10. s. 55 W. 64.60 4. N. 41 35 W. 6.15 llj s. 25 W. 18.12 5. N. 3 W. 36.75 Acres Roods Rods. 6. S. 86 50 W. 13.33 Area 97 — 2 — 29 7. N. 2 15 V^ 17.65 8. N. 85 45 E. 12.56 No. V. Rods. 9. S. 2 10 E. 8. 1. S. 11°50' W. 34.6 10. N. 86 45 E. 7.38 2. S. 63 20 E. 93 6 11. S. 3 15 E. 13.20 3. N. 4 w. 34.9 12. N. 87 E. 29.92 4. S. 89 55 E. 40.1 13. N. 49 20 E. 4.04 5. N. 5 20 W. 35.5 14. North 2.23 6. N. 69 40 W. 60. 15. N. 50 85 E. 6.50 7. S. 78 I W. 30.6 16. S. 22 50 E. 17.94 8. N. 67 20 W. 1.2 17. s. 34 W. 3.50 9. S. 72 30 W. 10.4 18. s. 41 W. 3. 10. S. 66 55 W. 15.^ 19. s. 22 50 W. 9.25 Acres Rood Rods. 20. s. 3 40 E. 2.64 Area 41 — 1 -34 1 21. s. 86 W. 2.50 22. s. 25 W. 14.50 No. VI . Rods. 23. s. 2 W. 5.38 1. S. 34° 0' E. 42.8 24. s. 10 E. 11.75 2. S. 29 E. 69.4 25. s. 86 W. 34.60 3. s. 64 50 W. 53. Acres Roods Rods 4. s. 25 E. 4. Area 268—3 — 7 5. s. m 30 W. 39. 6. N. 25 W. 4. No. VIII. Rods 7. S. 64 45 W. 32.2 1. S. 6°30' E. 19.1 8. N. 30 30 W. 18.3 2. s. 63 30 E. 14.36 9. N. 56 30 E. 34.5 3. s. 67 E. 10.68 10. N. 64 E. 12.5 4. N. 88 E. 13.3 11. N. 49 E. 14. 5. s. 3J 30 W. 32.44 12. N. 26 10 W. 19.3 6. s. 31 55 W. 96.5 13. N. 21 w. 18.3 7. s. 33 25 W. 34.9 14. N. 44 10 W. 18. 8. s. 20 45 E. 3.68 15. N. 64 40 E. 30.5 9. s. 16 15 W. 64. 54 SURV EYI? sG. 10. N. 52°30' W. 12.8 21. N. 36^ 0' E. 41.56 11. S. 45 w. 13.24 22. S. 6S E. 80.6 12. s. 69 w. 21.4 23. N. 44 30 E. 20.4 13. s. 12 40 w. 9.4 24. N. 2 30 W. 41. 14. s. 84 20 w. 9.5 25. X. 14 45 W. 62.32 15. N. 22 15 w. 24. 26. N. 16 W. 14.8 16. North 9,8 27. N. 1 45 W. 14.8 17. N. 29 15 w. 30.6 28. N. 82 30 W. 99. 18. N. 44 25 w. 21.8 19. N. 61 30 w. 23.1 A cres Rood Rods 20. N. 41 w. 10.8 Area 135 — 1 — 15 CASE v. To SUEVEY A FIELD FROM ONE STATION AT A>'Y PLVCE WITHIX THE FIELD, FRO:?I -^VHICH THE SEVERAL ANGLES MAY BE SEEX. Take the bearing of the angles, and measure their dis- tance from the station. FIELD BOOK. See Fig. 56. Fis. 56. Ch. L. From station to A. N. 20 °W. 8.70 B. N. 60 E. 10. C. X. 87 E. 11.40 D. s. 15 E. 10.50 E. s. 60 W. 12. F. X. Qb W. 8.78 TO PROTRACT THIS FIELD. Draw a meridian line as X S. From some point in that line as a centre, lay off the bearing and distance to the sev- eral angles, and draw lines from one angle to another, as AB, BC, CD, &c. SURVEYING. 55 TO FIND THE AREA. The Area may be calculated according to prob. XII. by measuring diagonals and perpendiculars ; or more accurately according to prob. IX. Rule 4. As the bearing and distance of the lines from the station to the several angles are known, two sides and their contained angle are given in each of the triangles into which the plot is divided ; the area may, therefore, be readily calculated by the RULE above referred to. Note. As in the operation, the logarithm of radius is to be subtract- ed from the sum of the other logarithms, it may be done by rejecting the left hand figure, without the trouble of putting down the ciphers and subtracting. Triangle aAB. aA,8.70 - - - 0.939519 aB, 10 - - - 1.000000 SineAaB,80° - - 9.993351 Doub. area, 85.67 Triangle aBC. aB, 10 - - - aC, 11.40 Sine BaC, 27° Doub. area, 51.75 Triangle aCD. aC, 11.40 aD, 10.50 - SineCaD,78<» - Doub. area, 117 - 1.932870 1.000000 1.056905 9.657047 1.713952 1.056905 1.021189 9.990404 2.068498 Triangle aAB aBC aCD aDE aEF aFA Double area Area aD, 10.50 aE,12 Sine DaE, Doub. are aE, 12 aF, 8.78 Sine EaF, Doub. are aF, 8.78 aA, 8.70 Sine FaA Doub. Ar Triangle 75° - a, 121.7 Triangle 55° - a, 86.31 Triangle 45° ea, 54.01 Acre Area2l aDE. - 1.021189 - 1.079181 - 9.984944 - 2.085314 aEF. - 1.079181 - 0.943495 - 9.913365 - - 1.93«)41 aFA. - 0.943495 - 0.939519 - 9.849485 - 1.732499 85.67 51.75 117.1 121.7 86.31 54.01 827 4 3)308 40 12)320 s Roods Rods > — 3-12.32 516.54 25)827 56 SURVEYING. CASE VI. To SUEVEY A FIELD FROM SOME ONE OF THE ANGLES, FROM WHICH THE OTHERS MAY BE SEEIY. From the stationary angle take the bearing and distance to each of the other angles, with a compass and chain. Fig, 57. C FIELD BOOK. See. Fig, 57. ' Ch. L. FG. N. 70° W. 14.60 FA. N. 50 W. 18.20 FB. N. 30 W. 16.80 FC. N. 10 W. 21.20 FD. N. 7 E. 16.95 FE. N. 30 E. 8.50 To DRAW A PLOT OF THIS FIELD. Draw a meridian line to pass through the stationary angle as at F. From the point F, lay off the bearing and distance to the several angles, and connect them by lines, as FG, FA, FB, &c. The area may be calculated as taught in the preceding CASE. CASE VII. To SURVEY A FIELD FROM TWO STATIONS WITHIN THE FIELD, PROVIDED THE SEVERAL ANGLES CAN BE SEEN FROM EACH STATION. SURVEYING. 57 Find the bearing from each station to the respective an- gles ; and also the bearing and distance from one station to the other. Fig. 58. FIELD BOOK. See Fig. 58. First Station. AC. N. 38° 30' E. AD. S. 69 E. AE S. 59 W. AF. N. 63 W. AG. N. 21 w. AH. North. Second Station. BC. S. 82° 0' E. BD. S. 17 E. BE. S. 28 W. BF. S. 49 W. BG. N. 76 W. BH. N. 24 W. Stationary line AB. N. 14° E. 20 chains. To PROTRACT THIS FIELD. At the first station A, draw a meridian line and lay off the bearings to the respective angles ; draw the stationary line AB, according to the bearing and distance ; at B, draw a meridian line parallel to the other, and lay off the bearings to the angles, as taken from this station ; from each station draw lines through the degree which shows the bearing of each angle, as marked by the protractor or line of chords, and the points where those lines intersect each other will be the angles of the field. Connect those angular points to* gether by lines, and those lines will represent the several sides of the field. CASE VIII. To SURVEY AN INACCESSIBLE FIELD. Fix upon two stations at a convenient distance from the F 58 SURVEYING. field, from each of which the several angles may be seen ; from each station take the bearing of the angles ; and take the bearing and distance from one station to the other. Fig. 59. FIELD BOOK. See Fig. 59. j •r/c Second Station. B BE. N. 50° 0' W BF. N. 29 15 W. BD. N. 24 w BG. N. 21 30 w BH. N. 5 E. BC. N, 20 30> Ch. L. E. First Station. AE. N. 9° 15' E. AF. N. 16 E. AG. N. 14 30 E. AD. N. 39 E. AH. N. 40 E. AC. N. 72 E. Stationary distance AB, S. 88° 30' E. 19.20. The directions given in the last case for plotting the field, will apply in this case also ; and the area in this and the pre- ceding CASE may be calculated in the manner pointed out in CASE IV. by dividing the plot into triangles and measuring diagonals and perpendiculars. Or the sides may be found by trigonometry, and the area calculated arithmetically, as al- ready taught. CASE IX. To SURVEY A FIELD WHEBE THE BOUNDARY LINES ARE SURVEYING. VERY IHREGULAR, WITHOUT NOTICING WITH THE COMPASS EVERY SMALL BEND. Begin near one corner of the field, as at A, f'ig. 60. and measure to the next large corner, as B, in a straight line ; noticing also the bearing of this line. From the Une take offsets to the several hends, at right angles from the line ; noti- cing in the field book at *j- what part of the line they are taken, as at A 1 , H 2, 1 3, B 4. Proceed in the same man- ner round the field. In the figure the dotted lines rep- resent the stationary lines, Sj^ and the black lines the boun- ' daries of the field. Fig. 60. Bearing and Distance. Offsets Bearing and Distance. Offsets Ch.L. AB. N. 85° C E. 11.20 at 5.40 8.26 the end Ch. L. 0.56 1.40 0.36 0.36 Ch.L. EF. S. 67° 50' W. 8.20 at 1.04 2.96 5.88 the end Ch. L. 0.40 0.36 0.33 1. 0.12 BC. N. 7° 20' E. 7.96 at 2.36 4.28 the end 0.20 0.36 0.96 0.30 FG. S. 270 40'E. 7.06 at 2. the end 1.20 0.24 0.16 CD. N. 62° 0' W. 4.68 at 4.34 0.30 GA. S. 25° 20' W. 6.48 at 3.80 the end 0.80 0.40 DE. N. 11° 10' W. 4.20' 0.30 To PROTRACT THIS FIELD. Draw the stationary lines according to the directions in CASE IVc- From A make an offset of 56 links to I ; measure from A to H 540 links, and make the offset, H 2, 140 links ; measure from A to I 826 links, and make the offset I 3, 36 links at B make the offset B 4, 36 links. Proceed in the same manner round the field, and connect the ends of the offsets bylines, which will represent the boundaries of the field. 60 SURVEYING. To FIND THE AREA. Find the area within the stationary lines as before taught ; then of the several small trapezoids, rectangles, and trian- gles made by the stationary lines, offsets, and boundary lines, and add the whole together : thus, add 56 links the offset A 1 to 140 links the offset H 2 and multiply their sum 196, by half 540, the length of the line AH, and the product, 52920 square links, will be the area of the trapezoid AH21 ; again, add 140, the offset H 2 to 36, the offset I 3, and multiply their sum, 176, by half 286, the length of the line HI, and the pro- duct, 25168 square links, will be the area of the trapezoid HI32. Proceed in the same manner to calculate the area of all the trapezoids, triangles, &;c. CASE X. To SURVEY A FIELD BY TAKING OFFSETS BOTH TO THE RIGHT AND LEFT ; THAT IS, WITHIN AND WITHOUT THE FIELD, AS OCCASION SHALL REQUIRE, IN CONSEQUENCE OF THE STA- TIONARY LINES CROSSING THE BOUNDARY LINES ; ALSO, BY IN. TERSECTIONS, THAT IS, TAKING THE BEARING OF AN INACCES- SIBLE CORNER FROM TWO STATIONS. The directions given in the preceding case, together with the following field book, will show the learner how to sur- vey a field like the following, and also to protract it when surveyed. SURVEYING. 61 Fig. 61, FIELD BOOK. See Fig, 61. Offsets to the Left Ch. L 1.12 3.40 1.25 Bearing and Distance. Offsets to the Right Remarks. Ch. L. AB. iN. 88° 0' W. 22.12 at 4.25 7.40 13. Ch. L. 1.20 1.15 A tower bears from A. N. 48S W. 0.45 BC. N. 27° 45' W. 21.12 at 4.10 10.25 15. From B the tower bears N. 38° 30' E. C 1. S. 82° 15' E. 5.45 1 2. N. 70 E. 13.25 2 D. N. 20 E. 3.36 From C go into the field to 1, on account of some impediment oh or near the boundary hne. At D, you get into another corner of the field. DF.S. 35°0'E. 15.15 E, an inaccessible corner, bears from D, S. 65° 30' E. 2.20 2.32 FA. S. 15° 15' E. 15.10 at 1.20 7.45 12.25 0.36 E, the inacessible corner, bears from F. N. 4° W. Note. — To draw a tree, house, tower, or any other remarkable object, in its proper place, in the plot of a field — from any two stations, while surveying the field take the bearing of an object, and the intersection of the lines, which represent the bearings, will determine the place of the object, in the same manner that the tower is drawn in the figure. F2 9^ SURVEYING. To FIND THE AREA OF THE ABOVE FIELD. Find the area within the stationary Hnes, and then of the several small trapezoids, &;c. remembering to distinguish those without the stationary lines from those which are with- in. Subtract the area of those within the stationary lines from the area of those without, and add the remainder to the area contained within the stationary lines ; the sum will be the whole area of the field. [Or, add the areas of those without the stationary lines, to the area contained within those lines, and subtract from the sum, the areas of the several triangles, trapezoids, &;c. within the stationary lines.] SECTION III, Rectangular surveying, or an accurate method of calcula- ting THE AREA OF A FIELD ARITHMETICALLY, FROM THE FIELD BOOK, WITHOUT THE NECESSITY OF PROTRACTING IT, AND MEASURING WITH A SCALE AND DIVIDERS, AS IS COMMONLY PRACTISED. I. Survey the field in the usual method, with an accurate compass and chain, and from the field book set down, in a traverse table, the course or bearing of the several sides, and their length in chains and links, or rods and decimal parts of a rod ; as in the 2nd and 3d columns of the following EXASCPM. SURVEYING. 63 d Oi 05 ■^ U5 1'"' 5S * r-t g 1 o *l ^ r^ n CO CO o> CO ^< • • CO CO o< 1 o CO ^ ^2 s^ s ? U5 . . . IT) T-H ©^ T}' CO CO •rf Oi Oi S^ t- CO ^ CO ^ ^ t- o =^6 o lo d a> OS Oi lO .,_, G^ CO s^ lO CO G< CO G* ©♦ T-l &. . -^ (?< CO s^ (N O "o-:? }> 1> i> t- o Gw O tfj lO "-^ "<* ■^ o M G^ ^ i> 00 oo '^ s^ JH . o in (T> LO LO S^ Tf G< • • • 05 l> t- oo < ^ • .' ^ • .* ^^ 1315 g^gJ CO CO O G^ CO t- t-H Tt* Lf> 00 o -^ Tjt CO K t- t- G^ GO oo U5LO • • gg i;i; ^^ a> a • • • • CO CO 1 CO lO 1 o o Ifl 1-H s? • • i O rH rH G* 02 • . Oi 05 •^ Tjl • S^ s^ • ITS LO , . , Tf -^ u: lO . GO GO GO 60 i>~»ri GO CO ' o ic 1 952 (N T-H t- CO 1 • • t- CO 25 t- t- T-H 1— 1 • • • • CO CO gg t- t- GO GO • • o o G< G^ ^ o O o o Tf< o CO '^ GO ^ LO ^ ^ GO 02 H W H ^ ^' o o ^ o I ^ i2 VO 5X -4-^ .,_( ■^ s ^ CO CO u ^ !z5 T-H z6 o Xfl CO No. T-( G^ GO •^ U2 CO c- C3 19143.9019 Sum of South Areas 4245.4016 North do. 2)14898.5003 Double Area of the Field. Acres 744)92501 4 Roods 3)70004 40 Rods 28)00160 Acres. Roods. Rods. Area 744—3 — 28 2. Calculate by right angled trigonometry, case I, or find by the table of difference of latitude and departure,* or * For an explanation of this table, and the manner of using it, see the remarks preceding the table. 64 SURVEYING. by the table of natural sines,* the northing or southing, east- ing or westing, made on each course, and set them down against their several courses in their proper columns, marked N. S. E. W. Note. To determine whether the latitude and departure for any paj- ticular course and distance are accurately calculated, square each of them ; and if they are right, the sum of their squares will equal the square of the distance, for the following reason : the latitude and de- parture represent the two legs of a right angled triangle, and the distance the hypothenuse ; and it is a mathematical truFh, that the square of the hypothenuse of any right angled triangle is equal to the sum of the squares of the two legs. 3. If the survey has beea accurately taken, the sum of the northings will equal that of the southings, and the sum of the eastings will equal that of the westings. If, upon adding up the respective columns, these are found to differ very con- siderably, the field should be again surveyed : as some error must haJV-e been committed, either in taking the courses or measuring the sides. If the difference is small, a judicious, experienced surveyor will judge from the nature of the ground, or shape of the field surveyed, where the mistake was most probably made, and will correct accordingly. Or, the north- ings and southings, and the eastings and westings may be equalled by balancing them, as follows : subtract one half the difference from that column which is the largest, and add it to that column which is the smallest ; and let the difference, to be added or subtracted, be divided among the several courses, according to their length. f In EXA2yiPLE I. the upper numbers are the northings, &;c. as found by a table of difference of latitude and departure. The several columns being added, the northings are found to ex- ceed the southinors 47 links, and the westings to exceed the eastings 24 links. [47 being uneven, drop a link from the northings, and it becomes 46. Let half of this ('23) be taken from the northings, and added to the southings ;] likewise, take 12 links from the westings, and add it to the eastings. Take from the first course of the northings 12 links, from the second 7, and from the third 5 ; to the first southing add 7 links, to the second 10, and to the third 6 ; add to the first easting 3 links, to the second 3, to the third 4, and to the fourth 2 ; take from the first westing 5 links, from the second 4, and from the third 3. [These are the proportional correc- * See the remarks preceding the table of natural sines. t This may be done by proportion, or the ride of three. If the dif- ference be an uneven number of links, drop a link from the greater number, and it will be rendered even.— Ed. SURVEYING. 65 tions belonging to each, as found by calculation.] The lower numbers will then represent the northings, &;c. as balanced. 4. These columns being balanced, proceed to form a de- parture column, or a column of meridian distances ; which shows how far the end of each side of the field is east or west of the station where the calculation begins. This column is formed by a continual addition of the eastings, and subtrac- tion of the westings ; or by adding the westings and subtract- ing the eastings : see examplf. I. The first easting, 20.74, is set for the first number in the departure column ; to this add 24.38, the second easting, and it makes 45.12, for the second number ; to this add 30.04, the third easting, and it makes 75.16, for the third number; to this add 9.56, the fourth easting, and it makes 84.72, for the fourth number ; the fifth course being south, it is evident the meridian distance will remain the same, therefore, place against it the same easting as for the preceding course ; from this subtract 39.95, the first westing, and it leaves 44.77, for the sixth course ; from thi^ subtract 23.75, the second west- ing, and it leaves 21.02, for the seventh course ; from this subtract 21.02, the last westing, and it leaves 0.0, to be set against the last course, which shows that the additions and subtractions have been accurately made. For as the eastings and westings equal each other, it is evident that one being added and the other subtracted, there will be in the end no remainder. 5. The next step in the process is to form a second depar- ture column, the numbers in which show the sum of the me- ridian distances at the end of the first and second, second and third, third and fourth courses, &c. The first number in this column will be the first in the oth- er departure column ; to which add the second number in that column for the second in this ; for the third add the se- cond and third ; and for the fourth, the third and fourth ; and so on until the column be completed. See example I. The first number to be placed in the second departure col- umn is 20.74 ; to this add 45.12, and it makes 65.86 for the second number ; to 45.12 add 75.16, and it makes 120.28, for the third number ; to 75.16 add 84.72, and it makes 159.88 for the fourth number ; to 84.72 add 84.72, and it makes 169.44 for the fifth number ; to 84.72 add 44.77, and it makes 129.49 for the sixth number ; to 44.77 add 21.02, and it makes 65.79 for the seventh number; to 21.02 add 0.0, and it makes 21.02 for the eighth number. 6. When the work is thus far prepared, multiply the seve- ral numbers in the second departure column by the northing* or southings standing against them respectively ; place th@ 66 SURVEYING. products of those multiplied by the northings in the column of north areas, and of those multiplied by the southings in the column of south areas ; add up these two columns and sub- tract the less from "the greater ; the remainder will be double the area of the field in square rods or square chains and links, whichever measure was used in the survey. [In the preceding explanations, the meridian is supposed to pass through the extreme west angle of the field. It is best always to take the extreme east or west angle.] Fig. 62. 3. 9 — l" Demonstration oj thepreceding rules. • See Fig. 62. and example I. The dotted line A 2 represents the northing, and the line 2 B the easting made by the first course ; these multiplied to- gether, that is, 77.15x20.74=1600.0910, which is double the area of the triangle A2B, as is evident from the rule to find the area of a triangle, prob. IX. Rule I. This number is to be placed for the first number in the column of north areas. The line 3C represents the sum of the eastings made by the first and second courses, which is 45.12 the second number in the first departure column ; if to this you add 20.74 the length of the line 2B you have 65.86, w^hich is the second number in the second departure column, and which represents the sum of the two lines 3C and 2B. These two lines with the line 2 3 which represents the northing made by the second course, and the line BC, one of the sides of the field, form a right angled trapezoid. Now, by the rule to find the area of such a trapezoid. See prob. X. 65.86x31.66=20 85.1276, double the area of the trapezoid 2BC3. Place this product for the second number in the column of north areas. To the line 3C add CD 30.04, the easting made by the third course, and you have 75.16. which is the sum of the SURVEYING. 67 eastings made by the three first courses, and the third number in the first departure column. To this add 9.56, the easting of the fourth course, and you have 84.72, the length of the line IE, which represents the sum of the eastings made by the four first courses, and is the fourth number in the first de- parture column. These two, viz. the lines 3D 75.16 and IE 84.72, added together make 159.88, the fourth number in the second departure column ; which, being multiplied by 49.15, the length of the line 3 1 which represents the southing made by the fourth course, will give double the area of the trapezoid lEDB. The number thus produced is 7858.1020, which is to be placed for the first number in the column of south areas. The fifth course being due south, it is evident the sum of the eastings will remain the same as at the end of the fourth course ; that is, the line 4F equals the line IE, which is 84.- 72. These added make 169.44, the fifth number in the sec ond departure column. This, being multipHed by 54.10, the length of the line EF, which is the southing of the fifth course as corrected in balancing, and the same as the line 1 4 will give double the area of the parallelogram 1EF4, which is 9166.7040, the second number in the column of south areas. From the line AF 84.72 subtract 39.95, which is a west course, and it leaves 4G 44.77, the sum of the eastings, or the meridian distance, at the end of the sixth course, and the sixth number in the first departure column. From this subtract 23.75 the westing made by the seventh course, and you have 21.02, the length of the line 5H, which is the meridian dis- tance at the end of the seventh course, and the seventh num- ber in the first departure column. The line 4G 44.77 added to the line 5H 21.02 make 65.79, the seventh number in the second departure column. This being multiplied by 32.21, the length of the line 4 5 which is the southing of the seventh course, will give double the area of the trapezoid 4GH5, which is 2119.0959, the third number in the column of south areas. The line H5, 21.02, is the westing of the last course, and the last number in the second departure column. This being multiplied by 26.65, the length of the line 5A, and the north- ing of the last course, produces 560.1830, which is double the area of the triangle A5H, and the last number in the col- umn of north areas. Note. It will be observed that against the third and sixth courses there are no areas ; the reason is, that these courses being one east and the other west, there is no northing or southing to be multi- 68 SURVEYING. plied into them : regard can therefore be had to them only in form- ing the departure columns. By inspecting the figure, and attending to the preceding illustrations, it will be seen that the three north areas repre- sent double the area of the triangle A2B, the trapezoid 2BC3, and the triangle A5H, all of which are without the boundary lines of the field : also, that the three south areas represent double the area of the trapezoid 3DE1, the parallelogram 1EF4, and the trapezoid 4GH5 ; and that these include not only the field but also what was included in the north areas. Therefore the north areas subtracted from the south, the re- mainder will be double the area of the field, contained with- in the black lines. Additional dieections and explanations. The northings and southings may be added and subtracted instead of the eastings and westings ; then there will be two latitude columns instead of departure columns, and the num- bers in the second latitude column must be multiplied into the eastings and westings, and you will have east and west areas. When the course is directly north or south, the distance must be set in the north or south column ; when east or west, in the east or west column. There will therefore sometimes be no number to be added to or subtracted from the number last set in the latitude or departure column ; then the number last placed in the column must be brought down and set against such course ; as in exat.iple I. at the 5th course. It may also sometimes be the case, that there will be no number to multiply into the number in the second latitude or departure column ; then that number must be omitted, and against such course there will be no area, as in example I. at the 3d and 6th courses. When the northings or southings, eastings or westings, be- ginning at the top, will not admit of a continual addition of the one and subtraction of the other, without running out before you get through the several courses, you may begin at such a course in the field book as will admit of a continual addition and subtraction; and when you get to the bottom go to the top, and you will end in cipher at the course next above that SURVEYING. 69 where you began : as in example II. which begins at the 9th course to add the eastings and subtract the westings.* Example II. r^o Courses. Dis. N. S. E. W. ^^ep. 2dep. North South 1 T. rods Uol. Col. areas areas N.75''0'E.154.8 14.2 .... 52.9! 144.] 235.3 S^4L2(i 1 2. N.20 30E. 41.2 38.6 .... 14.4 1585 302.6 11680.36 1 3. 4. 5. 6. East S.33 30W S. 76 OW North 64.1 141.2 64 36 36" 117.7 15.5 64.8 77.9 62.1 223.£ 145.4 83.£ 83.£ 381.8 1 368.7 43395.99 3544.85 228.7 , 166.6 5997.60 7. S. 84 W 46.4 49 . . . . 46.1 37.S 120.5 ' 590.45 8. N.5315W 46a 27.8 .... . . . . 37.2 O.C 37.2 1034.16 9. N.3645E. 16.h 61.5 .... 46 46 46 2829 1 10. N.2230E. 56 51.7 21.4 67.4 113.4 5862.78 11. S.76 45E. 48 11 46.7 ...... 114.] 181.5 : 1996.50 12. S. 15 W 43.4 41.9 11.2 102.S 217 9092.30 ± S.16 45 W 40.5 •— • 38.8' 11.7 91.S 191.1 ' 7531.08 Area 110 Acres, 2 Roods, 23 Rods. Note. In the above example you might begin at the 4th course to add the westings and subtract the eastings ; or at the 6th course to add the northings and subtract the southings : or at the 11th course to add the southings and subtract the northings. So in every survey, some place may be found w^here you may begin to add and subtract, without running out before you get through all the cours- es.* When a field is very irregularly shaped, it will often hap- pen that parts of the same area will be contained in several different products in the columns of areas ; but in the final re- suit, one column being subtracted from the other will leave what is included within the boundary lines of the field. * Much the most convenient method is to place the course at which you begin to add and subtract at the head of the field book. The surveyor may easily do this, by observing in the field, which angle of the field is furthest east or west, north or south. — Ed. G 70 SURVEYING. Fig, 63. L, 3\ 4- 8 Q, 3 Demonstration. ^ SeeFig.QS.andEx. ',! AMPLE II. ^• M The area standing against the 9th course^* which is where the calculation begins, is the triangle 12K, all without the field. The area against the 10th course is the trapezoid 2KL35 also without the field. The area against the 11th course is the trapezoid 4ML3. This is a south area, and contains a part of the field and also part of the preceding north area. The area against the 12th course is the trapezoid 5NM4j part within and part without the field. The area against the 13th course is the trapezoid 6AN5, part within and part without the field. The area against the 1st course is the trapezoid 6AB7, part within and part without the field. This is a north area, and to be ultimately subtracted from the south areas ; but this includes a part of the preceding south areas, viz. the space nAso ; it will, however, be seen hereafter that this same space is included in another south area. This north area contains also a part of the first north area, viz. the space 6no7 ; but the same space is also included in another south area. The area against the 2d course is also a north area, and is the trapezoid 7BC8. This trapezoid contains the space sBCx, without the field ; the space osxw, within the field ; and the space 7ow8, without the field. But the space os^xw will be contained in the next south area ; and the space 7ow8 which was contained in the two first north areas, will be con! tained in the next south area. By examining the whole figure in this manner, it will be * The numbering, here, corresponds not to the diagram, but to the jlELD-BOOK on the last page. After the 8th course, hkewise, in the en- graving, the numbers are incorrect, the true 9th course, DE^ being left without a number, and the others numbering 9, 10, &c. when they should be 10, ll,&c.— Ed. SURVEYING. 71 seen that the north areas contain all without the field that is taken into the calculation, and some of it twice over ; they also contain part of the area within the field. The south areas contain all within the field, and all without the field that is contained in the north areas. They also contain, twice over, so much of the field as is included in any of the north areas ; and likewise, twice over, that part without the field which is contained twice in the north areas. So that sub- tracting the north from the south areas leaves double the area of the field. This method of calculating the area of a field by the north- ings, southings, eastings, and westings, divides the field, with a certain quantity of the adjoining ground, into right angled triangles, right angled trapezoids, rectangles or squares, as may be seen by the figures. It may therefore with propriety be called rectangular surveying. A USEFUL PROBLEM. To FIND THE TRUE AREA OP A FIELD WHICH HAS BEEN MEASURED BY A CHAIN TOO LONG OR TOO SHORT. Calculate the area as if the chain was of a true length, then institute the following proportion : As the square of the length of the true chain ; Is to the area, as found by the chain made use of; So is the square of the length of that chain ; To the true area of the field. Example. Suppose a field, measured by a two rod chain 3 inches too long, is found to contain 41 acres 1 rood and 33 rods, what is the true area. As the square of 33 feet, the true length of a two rod chain ; is to 41 acres 1 rood and 33 rods ; so is the square of 33 feet 3 inches, the length of the chain used in the survey ; to 42 acres and 13 rods. 33 feet= 396 inches. 396x396 = 156816 square inches. 41 acres 1 rood 33 rods=6633 rods. 33 feet 3 inches— 399 inches. 399x399=159201 square inches. * 159201x6633-i-156316=:6733 rods 6733~-160=42 acres 13 rods, the true area. T2 SURVEYING. PART II. Laying out la.nd. PROBLEM I. To lay out any number of acres in the FORM OF a square. Annex 5 ciphers to the number of acres, which will turn them into square links, the square root of which will be the side of the square in links. Example. L It is required to lay out 810 acres in the form of a square. Answer. Each side of the 'square must be 9000 links, or 90 chains. PROBLEM II. To lay out any number of acres in THE FORM OF A RECTANGLE, WHEREOF ONE SIDE IS GIVEN. Divide the number of acres, when turned into square links, by the given side ; the quotient will be the side required. Example. What must be the longest side of a rectangle, which is to contain 25 acres, when the shortest side is 5 chains and 50 links ? Answer, 2500000—550= 4545 links for the longest side. PROBLEM III. To lay out any number of acres in a FIELD, 3, 4, 5, 6, &;c. times as long as it is broad. Divide the acres, when turned into square links, by the ra- tio between the length and breadth ; the square root of the quotient will be the shortest side. Example. It is required to lay out 100 acres 5 times as long as it is broad. Answer, 10000000-^5=2000000 the square root of which is 1414 links for the shortest side, and the longest will be 7070 links. PROBLEM IV. To make a triangle which shall con- tain A GIVEN number OF ACRES, BEING CONFINED TO A CER- tain BASE. Double the given number of acres, to which, annex 5 ci- phers, and divide by the base ; the quotient will be the per- pendicular height in links. Example. Upon a base of 40 chains to lay out 100 acress in a triangular form. Answer. 5000 links or 50 chains will be the length of th@ perpendicular. SURVEYING. 73 The perpendicular may be erected jfrom aay part of the base : thus, the triangle ABC, see Fig. 64. is the same as ABE, each containing 100 acres. When the given base is so situ- ated that a perpendicular of suf- ficient length cannot be erected therefrom, continue the base as from B to D, Jig. 65. from which erect the perpendicular DC, and complete the triangle ABC, which will contain 100 acres. ^ Fig. 65. PART III. j: : J Dividing land. As different fields are so variously, and many of them ir- regularly shaped, and as they are required to be divided in many different proportions, it is difficult to give rules which will apply to particular cases. The business of dividing land must therefore be left, in a great measure, to the skill and judgment of the surveyor ; who, if he is well acquainted with trigonometry, and with measuring land, will not find it diffi- cult, after a little practice, to divide a field in such a manner as shall be desired. If he has before him a plot of the field, and knows the number of parts into which it is to be divided, and the proportion which each part is to bear to the others, he will readily find out where the dividing lines are to be drawn. A few RULES and examples will be given for the general instruction of the learner. PROBLEM I. To cut off any number of acres from A SQUARE OR RECTANGLE. G2 74 SURVEYING. Say, as the whole number of acres in the field ; is to the length of4he square or length or breadth of the rectangle ; so IS the number of acres proposed to be cut off; to their propor- tion of the length or breadth. PROBLEM II. To cut off any number of acres by a LINE FROM ANY ANGLE OF A TRIANGLE. Measure the base, or side opposite the angle from which the dividing line is to be drawn ; then say, as the number of acres in the whole triangle ; is to the whole base ; so is the given number of acres ; to their part of the base. Fig. m. Example. See Fig, 66. In the triangle ABC, which contains 48 acres, it is requir- ed to cut off 18 acres, by a line proceeding from C to the base AB, which is 40 chains. As 48 : 40 : : 18 : 15 Lay 15 chains on the base from B to D, and draw the line CD. The triangle will then be divided as was proposed ; BCD containing 18 acres. PROBLEM III. To take off any given number of ACRES from a multangular FIELD. Fig, 67. D Example I. See Fig. 65. Let ABCD, &c. be the plot of a field containing II acreSy from which it is required to cut off 5 acres. Join two opposite corners of the field as D and G, with the line DG (which you may judge to be near the partition line) and find the area of the part DEFG, which, suppose, may want 140 rods of the quantity proposed to be cut off. Mea- SURVEYING. t5 sure the line DG, which, suppose to be 70 rods ; divide 140 by 35 the half of DG, and the quotient 4 will be the length of the perpendicular of a triangle, whose base is 70 and the area 140. Lay off 4 rods from G to i, and draw the line DI, which will be the dividing line.* Example If. See Fig. 68. Let ABCD, &c. be a tract of land to be divided into two equal parts, by a line from I to the oppo- site side CD ; to find arithmetical. ly on what part of the line CD the dividing line IN will fall ; or to find the distance CN. Ficr. G8. FIELD BOOK. Rods. AB. N. 19° 0' E. 108 BC. S. 77 E. 91 CD. S. 27 E. 115 DE. S. 52 W. 58 EF. S. 15 30 E. 76 Rods. FG. West 70.9 GH. N. 36° 0' W. 47 HI. North 64.3 I A. N. 62 15 W. 59 Acres Rood Rods Whole area 152 — 1 — 25 Find the area of the part lABC, according to section III. page 57, as follows : set the latitude and departure of the three first sides, lA, AB, and BC, in their proper columns, in a traverse table ; and place as much southing, viz. 109.1, equal to the line CK, and as much westing, yit.. 71.7, equal to the line KI, as will balance the columns. This southing and westing will be the latitude and departure made by the line CI. the area of lABC will be found to be 8722 rods, which is less than half the area of the whole field by 3470 rods, the quantity to be contained in the triangle ICN. * This explanation supposes DG and AG at right angles to each other. When they are not at right angles, the height GI must not be measured on the side of the field. — Ed. 76 SURVEYING. Find the bearing and distance of CI by right angled trig- ONOMETRY, CASE IV. aS folloWS :* As CK, the southing of CI, 109, nearly - - 2.037426 : radius . _ lO.OOOOOO ::KI, the westing of CI, 71.7 - - - - - 1.855519 11.855519 2.037426 : tangent courses. 33° 20' W 9.818093 As sine course 33" 20' 9.739975 • departure KI 71.7 1.855519 : : radius 10.000000 11.855519 9.739975 I Distance IC 130.5 2.115544 Note. In this way the course and distance may be found from any an^le of a lield to another. Having found the line CI, divide 3470, the number of rods to be contained in the triangle ICN, by one half the line CI, viz. 65.25 ; the quotient will be the length of the perpendic- ular PN, viz. 53.18. Now, by the bearings of CI and CD, it appears that they form an angle of 60° 20' ; wherefore, in the triangle CPN are given the side PN 53.18, and the angle at C 60^ 20', to find the hypothenuse CN. As sine PCN 60° 20' : side PN 53.18 : : radius : hyp. CN 61.2 9.938980 1.725748 10.000000 11.725748 9.938980 1.786768 Thus the dividing line must go from I to a point on the line CD, which is 61.2 rods from C. The bearing and dis- tance of this line may be found by the directions given above for finding the bearing and distance of the line CI. Or, they may be found by oblique trigonometry, case III. * The mode given above is undoubtedly the most correct, but the use of the traverse table will save many figures. From that table the course and distance of CI, may be found at sight.— Ed. SURVEYING. n Another method of finding the distance CN. Having ascertained the latitude and departure of the line CI, set them down in a traverse table ; find the latitude and departure of the line CD, and place them in the table ; the difference between the northing of the line IC, and the south- ing of the hne CD will be the southing of the line DI, viz. 6. 6 ; and the sum of the eastings of those lines, as they are both easterly, will be the westing of the line DI, viz. 123.9. Proceed to calculate the area of the triangle ICD, which will be found to be 6522 rods, nearly. Note. As in this triangle two sides and their contained angle are g-iven, the area may be found by prob. IX. rule 4, -page 40. Having found the area of this triangle, proceed to find CN according to prob. II. page 74, as follows : As the area of the triangle ; is to CD the base ; so is the quantity to be contained in the triangle ICN ; to CN its pro- portion of the base. As 6522: 115:: 3470: 61.19. A THIRD METHOD OF FINDING THE DISTANCE CN. To the logarithm of double the area to be contained within the triangle ICN add radius ; from this sum subtract the loga- rithmic sine of the angle at C ; and from the remainder sub- tract the logarithm of the side IC ; the last remainder will be the logarithm of the side CN. The double area of the triangle ICN is 6940 ; the anale at C is 60° 20' ; the side IC is 130. Double area 6940 - . 3.841359 Radius - - - 10.000000 13.841359 Sine ICN 60° 20' . • 9.938980 3 902379 Side IC 130.5 . - 2J15544* Side CN 61.21 - - 1.786835 * The lof. of IC, as found by calculation on page 76, is employed, instead of taking from the tables, that of 130.5, which is not the exact length of IC.—Eo. 8 SURVEYING. Note. Radius may be added by placing a unit before the index of the logarithm for the double area, without the trouble of setting down the ciphers. Br ^ATUKAL SIXES. Divide the double area by the natural sine of the given an- gle, and that quotient by the given side : the last quotient will be the side CX. Nat. sine of the ande at C 60^ 20' 0.86892 6940-^0.36892= 7 9S6.92 7986.92—130.5=61.2 From the above the follo\ving general rule may be drawn. to fixd the side of a teiaxgle whe^" the area is giv- zx, and also oxte of the sidesj and the angle coxtaixed between the given side ajst) the side requieed. to the l0gaeith3i of double the area add radius ; from this 3u3i subtract the logarithillc sine of the given angle, and from the re^iain^der subtract the log- arithm! of the given side ; the last remainder will be the logarithm of the side required. Or, By natural sines : divide the double area by the NAT. sine of the GIVEN ANGLE, AND THAT QUOTIENT BY THE GTVEN SIDE : THE LAST QUOTIENT WILL BE THE SIDE REQUIR- ED. CONCLUDING REMARKS. Other methods of surveying fields are tautrht by some authors on this subject. The preceding, however, will be found most useful in actual practice. Other instruments be- sides those mentioned in this book are sometimes used ; such as the plain table, semicircle, perambulator, theodo- lite, ike. But of these instruments very little use is made in New-England ; and they are not often to be met with. For general practice none will be found more useful than a com- mon chain, and a compass upon Rittenhouse's construction. A surveyor should also provide himself with an offset staff, ten SURVEYING. 79 links in length, and accurately divided into links. This should be made of firm hard wood, and will be found very conveni- ent in taking offsets, and also in measurmg the chain ; which should be often done, as from a variety of causes a chain is li- able to become inaccurate. It will be observed that in this work there are no descrip- tions of mathematical and surveying instruments. The com- piler omitted such descriptions from a belief that nothing which can be written on the subject will enable a person to un- derstand them without an actual inspection of the instruments themselves, and some instruction from those acquainted with them. The general principles here taught may be applied to the surveying of townships, roads, rivers, harbours, &c. mtWi APPENDIX. Of the declination a>-d variation of the magnetic keedle, and of the attractions to which it is srsject. The declination of this needle is the number of degrees it deviates from the true north, either east or west. This differs in different places, and in the same place at different times. [At Hartford, Conn, the declination was, in 1829, 6^ 3' west of the true meridian of the earth ; and was increasing by an annual variation of about 3'.] The following method of ascertaining the variation, by the north star has been adopted by many surveyors, as the most eligible to be practised on land. It was communicated to the compiler by Moses Warren, Jun. Esq. of Lyme, an ex- perienced surveyor, with permission to publish it. The star commonly called the north star, is not direcdy north but revolves round the pole in a small circle, once in 24 hours.* It can therefore be due north only twice in that pe- riod ; and that is within a very few minutes of the time, when a star, called AJiotJi in the constellation of Ursa major, or the great bear, is directly over or under it. There is also anoth- er star nearlv in an opposite direction from the pole, called Gamma, in the constellation of Cassiopeia. When thes^ three stars are vertical the north star is very near the merid- ian ; and when they are horizontal, it is at its greatest elon- gation, that is, at its greatest distance east or west of the pole, and on the same side as the star in Cassiopeia. The variation may be calculated when the star is on the meridian, or when at its greatest elongation ; more accurately, howev- er at the latter period, because its motion being then nearly * More exactly, 23 hours, 56 minutes and 4 seconds. — Ed. APPENDIX. 81 vertical for some time, gives the observer opportunity to com. plete his observation.t To find the elongation of this star in any latitude, its declination must be known ; that is, its distance north of the equator. This being found, institute the following propor- tion : As co-sine of the latitude ; is to radius ; so is co-sine of the declination ; to sine of the elongation.* The declination of the north star, January 1, 1810, was 88^ 17' 28", and increasing at the rate of about 19 seconds and one half annually. In the following table, the elongation is calculated for ten successive years, ending with 1840, and for seven different latitudes. The calculation is made for the first of July, and of course gives the mean angle for the year. Table showing the elongation op the north stab. Years. 32° 34° 36° 38° 40° 42° 44° 1831 10 521' 1° 55' 1 c > 581' 2c H' 2 5' 2 9 2 13 1832 52" 1 541 58 2 1 2 4i 2 8^, 2 121 1833 5H 1 54 57i 2 Oi 2 4 2 8 2 121 1834 51 1 53i 57 591 2 4 2 "7^ 2 12 1835 501 1 53 561 59 2 3 2 H 2 11 1836 50 1 521 56 581 2 21 2 6 2 101 1837 501 1 521 551 581 2 2 2 H 2 10" 1838 50 1 521 55 58" 2 n 2 5 2 91 1839 491 1 52" 541 571 2 1 2 H 2 9' 1840 1. 49 1 511 1, 54 JL 571 2 01 2 _£ 22 81 * This angle is usually called azimuth. — Ed. + The following figure exhibits a view of the relative situation of these stars, as they appear, when in a horizontal position ; or when the north star is in its greatest eastern elongation. The Great Bear. Cassiopeia. * * ^ Alioth Pole * N. star Gamma ^ ^ H 82 APPENDIX. The elongation for the latitude of the observation being calculated, or taken from the above table, proceed to find its range, according to the following directions ; Take a pole 18 or 20 feet in length ; to the end of it fast- en a small line ; raise it to an elevation of 45^ or 50° ; and support it by two crotches of suitable height to keep it firm in its place. At the end of the line near the ground, fasten a weight of half a pound or more, which should swim in wa- ter to prevent the air from moving the line. Southward of the line fix a compass sight, or other piece of metal or wood, with a narrow, perpendicular aperture at a convenient height from the ground, say about 2 or 2 1-2 feet ; and let it be so fixed that it can be moved a small distance east or west at pleasure. Let an assistant hold a hght either NE. or NW. of the line, nearly as high as the range from the sight to the north star, in such a position that the line may be plainly seen ; then, (the three stars above mentioned being parallel or nearly so with the horizon) move the sight-vane east or west, until through the aperture, the line is seen to cut the star ; and continue to observe, at short intervals, till the star is seen at its greatest elongation. Let a lighted candle be placed in an exact range with the sight-vane and line at the distance of 20 rods or more, which should stand perpendicu- larly, be made fast, extinguished, and left till morning. Then the sight-vane, the line, and the candle, will be the range of elongation, which observe accurately with a compass ; and if the elongation be east and the variation west ; the former must be subtracted from the latter ; and if they are both west they must be added, and their difference or sum will be the true variation.^ Of the attraction of the needle. It is well known that any iron substance has an influence upon the magnetic needle, attracting it one way or the other upon the point where it would settle, were there no such attraction. A surveyor should therefore be careful to see that no iron is near the compass when taking a bearing. But as the earth in certain spots contains, near its surface, iron or other minerals, which attract the needle, it will frequently happen that it will point wrong. To ascertain whether this is the case, the surveyor, at each station, should take a back * The author, in common with many writers, employs the term va^ riation^ as synonymous with declination. Variation is properly, how- ever, the change ofdeclinaiion.^ED. APPENDIX. 83 view of the one last left ; and if he finds that the compass does not reverse truly, he may be sure, provided the compass be accurately graduated and placed horizonally, that he ei- ther made a mistake at the last station, or that in one or the other or both of the stations, the needle was attracted from the true point. When he finds a place where he suspects there is an attraction, he should go a few rods backward or forward, and see whether the needle points differently. In this way he may prevent mistakes in his field notes, which would arise from putting down a wrong course. To take back sights is particularly necessary in running long lines, and laying out new lands, where the needle is the only thing to guide the surveyor. By practice and experience a knowledge will be acquired on this subject, and with regard to many other things in sur- veying, which cannot be taught by books ; and after all the directions which can be written, the practitioner will fre- quently find occasion for the exercise of his own judgment. A RULE TO FIND THE DIFFERENCE BETWEEN THE PRESENT VARIATION OF THE COMPASS, AND THAT AT A TIME WHEN A TRACT WAS FORMERLY SURVEYED, IN ORDER TO TRACE OR RUN OUT THE ORIGINAL LINES. Go to any part of the premises where any two adjacent cor- ners are known ; and if one can be seen from the other, take their bearing ; which compared with that of the same line in the former survey, shows the difference. But if one corner cannot be seen from the other, run the line according to the given bearing, and observe the nearest distance between the line so run, and the corner ; then work by the following pro- portion : As THE LENGTH OF THE WHOLE LINE, Is TO 57.3 DEGREES,* so is the said distance, to the difference of variation required. Example. Sappose it be required to run a line, which, some years ago, bore N. 45° E., distance 20 chains, and in running this line by the given bearing, the corner is found 20 links to the left hand ; what is the present bearing of this line ? * 57.3 degrees is the radius of a circle (nearly) in such parts that the circumference contains 360. 84 APPENDIX. Ch. Deg. L. As 20 : 57.3 : : 20. 100 20 2000 1146.0 60 2000)6S760(34 Minutes. Answer — 34 minutes to the left hand is the allowance re. quired, and the line in question bears X. 44^ 26' E. The compiler of this work acknowledges himself under ob- ligations to George Gillet, Esq. Surveyor General of the state of Connecticut, for the following illustrations, remarks. and miscellaneous questions, considering them calculated to be useful to the learner, and the practical surveyor. They came to hand too late to be inserted in their proper places, in the body of the work, and are here put together in the appen- dix. Remarks on the ikeeguiarities of the mag>-etic ^-EE. DLE. By a statute of this state, applicants for the appointment of county surveyor are required to be well skilled in the theory of the most approved method of surveying lands. It is also as necessary that they should be as well skilled in practical survepng. Practical knowledge must be acquired by expe- rience ; but no one can have a thorough knowledge of cor- rect practice vvithout being made acquainted with the imper- fections and irregularities of the magnetic needle. It is supposed, by most people, that this instrument, in all places, points exactlj- towards the poles of the earth, and that its direction remains as permanent as the poles themselves — an infallible guide.* This is a mistaken idea. A few re- marks on this subject will here be offered, and some facts re- specting it stated. * There is one line around the globe on which there is no variation. The general course of this line, on this side of the globe, is from north- west to southeast, but is crooked and irregular in its course. Accord- ing to Dr. Holly's chart, made in 1700, the line of no variation crossed the meridian of London in 55'^ south latitude — crossed the equator in 170 \v. longitude — from thence, by various windings, to the island of Bermuda, from thence nearly a west course until it struck the conti- APPENDIX, 85 Notwithstanding the great utility of the magnetic needle, it cannnot be relied on where great accuracy is required, on account of the irregularities to which it is subject, viz. its an- nual and diurnal variations, and what is the cause of still ncnt near Charleston, in South Carolina. This line is not stationary, but is ever varying its position ; and, notwithstanding the irregularity of its courses, it never crosses itself. About 1756, another variation chart was made, when it was found that the line had fallen so far to the west that it struck the continent near the coast of Florida. On the east side of this line, the magnetic needle points to the west of north, and on the west side it points to the east of north, and a regular in- crease of either east or west variation is found from it, on it^ op- posite sides. The line of no variation now runs through Penn- sylvania, and not far from Norfolk, in Virginia. When the Connec- ticut Western Reserve was surveyed into townships, the variation at that place was easterly from one to two degrees. In 1813, at New-Or- leans, the variation was easterly, about eight or nine degrees. In 1701, at Philadelphia, the variation was westerly, eight degrees and a half. In 1794, at the same city, the west variation had diminished to one degree and a half, Avhich proves that the progress of the line of no variation had been from west to east. In 1813, by observations at this city, it was found that the west variation had increased to about two or three degrees. By a series of observations, commenced at Hebron in Connecticut, by the writer of this, in 1805, and continued to 1813, it was found that the west variation during that period increased more than half a degree. The result of these observations agrees with those at Philadelphia, that there had been a retrograde motion of the needle. Since 1813, the west variation had diminished, or certainly it has not increased. The west variation at Hebron is now (1825) a few minutes more than five degrees. In 1580, at London, the magnetic needle pointed eleven degrees and a half to the east of north, which proves that the line of no variation was east of that place. The east variation diminished until 1657, when the line of no variation arrived there and soon passed by ; of course west variation began, and continued to in- crease until 1806, when it exceeded twenty-four degrees. The line of no variation must have had a rapid progress through the Atlantic and through a great part of the United States, to havs arrived at Charleston in 1700, and at the coast of Florida in 1756. The pres- ent bearing of all old lines in this state prove that there has been a con- siderable decrease of west variation since the first surveys were made ; which also proves that the progress of the line of no variation, in the United States, has, for a long time, been from west to east. How far the line of no variation progressed westward in the interior of this country before it turned, no one can tell. It is unaccountable how the west variation in London should increase, while at Philadelphia it was diminishing, when both places are on the same side of the line of no variation. The variation of the needle has long been a subject of much perplexity. Observations have been made in abundance. Many facts have been ascertained, but the difficulty is, they are not reducible to system. The polarity of the magnetic needle, with its variations and irregularities, is a hidden mystery, which is never to be searched out by man. It is sufficient in itself, without any other evidence, to cause the reflecting mind to wonder at, admire, and adore the wisdom, kno)vl- edge, and power of HIM who planned and directs it. H2 66 APPENDIX. greater perplexity, its local attractions. Whe:i an old course is given, to renew a line, it cannot be depended on, on ac- count of the change in declination, between the time of the first running, and the renewal of the line. No annual rate can be fixed on for the variation of the mag- netic needle, as its motion is much more rapid in some years than in others. By observations made at London during a period of more than two hundred years, it appears that in some years the motion of the needle Vas rapid, in others, but little could be discovered, and, in some years, the motion was retrograde. There is no regularity in its motion in any place. Another difficulty in retracing a line from an old course or from one recently given is, that it is often found that two com- passes do not make the same course. It was well known to the celebrated Rittenhouse, that his compasses did not all agree, or make the same course, and he was never satisfied as to the reason of it. It has also been ascertained that dif- ferent needles do not point alike at the same place. French writers on magnetism, have lately treated on this subject. Two compasses may differ a quarter of a degree or more or less, when no defect can be discovered in either. A survey may be taken as correctly with one as the other. The ques- tion then naturally arises, which of the two is right ? The answer is, both are right ; neither of them points directly to the poles of the earth, except on the line of no variation.* All that can be said of them is, that one has a greater varia- tion than the other, and that which has the least cannot have the preference. The diurnal motion of the magnetic needle is another defect in it. As the sun rises in the forenoon, * Both are certainly right, for there can be no doubt that the mag- netic axes in each, in most cases, arrange themselves accurately in the direction of the magnetic poles of the earth. Is it not rational to sup- pose, then, that one or both of these axes is slightly oblique to the di- rection of the needle ? A similar deviation might be produced, incase the magnetic axis should lie on one side of the pivot on which the nee- dle rests. The stronger attraction of the nearer pole 'uould cause a va- riation tovrards the opposite side. But whatever may be the cause of disagreement between compasses, it is not to be supposed that it would cease to act on the Ime of no variation. Compasses which differ in one place, will probably differ the world over. As the cause of this difference operates with uniformity, it is easy to understand that a sur- vey may l-e as accurately taJien with one, as with the other : but that should decidedly have the preference, the direction of which most near- ly corresponds with the known declination at the place. A survey, ta- ken by a needle which deviates from this, may be a fruitful source of lit- igation, when it is endeavoured to retrace the boujadaries with a more accurate instrument. — Ed. APPENDIX. 87 and the earth becomes heated, it has an effect on the unknown something which gives polarity to the needle, and turns the north end of it to the west. In the afternoon and night fol- lowing, the needle returns to its position. For several years, the writer made observations with a Rit- tenhouse's compass, to ascertain the diurnal motion ; and in the summer season usually found it about a sixth part of a de- gree. In the winter little or none could be discovered. The diurnal motion of the needle has been known in Europe about a century. f Local attraction, is likewise, one of the causes of the irregularities, to which the magnetic needle is subject. This is found oftener in hilly, broken lands, filled with ledg- es, than in level, feasible land, where there are no ledges. As the sources of attraction are generally out of sight, ther situa- tion should be determined by experiment. They sometimes cause the needle to deviate more than a degree, and often oc- casion a more trifling inaccuracy. The writer has known a dif. ference of more than five degrees within a distance of 40 rods. When an old line is to be renewed, where the bounds have been lost, the surveyor may verify or prove his accuracy in various modes. If he finds, for example, that the lots on each side of his line contain their due quantity, or possess their full width, he will have reason to believe that the line is accurately run : if not, he may allow for the excess or defi- ciency in either of these lots, and thus discover the true po- sition of the line. It would be difficult to mention all the circumstances which may govern, or which may serve as ev- idence in such cases. After all, the magnetic needle is the best guide that has yet been discovered, and it cannot be dispensed with in land surveying ; but the surveyor who is best acquainted with it, will make as little use of it as he can. In small surveys, where one angle may be seen from another, the quantity of each angle may be taken by an instrument constructed for that purpose, without the use of the magnetic needle ; and the sides may be measured, and one side, no matter which, may be made a meridian, and from that meridian courses may be calculated for the other sides, and the survey may be calculated by the rules of rectangular surveying. This me- thod has been recommended by theorists, and the ingenuity displayed in the invention, together with the correctness of it, so far as it is practicable, must be acknowledged ; but in lar- ger surveys, it cannot be introduced to practice, on account of the obstructions which often intervene betweenthe angular point and the terminations of the two contiguous lines which contain t The diurnal motion is mentioned in Dr. William's History of Ver- mont. APPENDIX. the angle : in such cases, the danger in taking the quantity of an angle will be greater than with the magnetic needle.* If in every town in the state, a meridian line was establish- ed by the motion of the heavenly bodies, and such meridians were perpetuated by durable monuments, whenever a survey was to be taken in the vicinity of a meridian, a surveyor might set his compass on it and note the variation found, and that variation should be inserted in the deed or in whatever wri- ting or instrument by which the land is conveyed and made a record ; this would assist a surveyor at any future period in retracing those lines, by setting his compass on the same me- ridian and allowing the same variation that was allowed when the survey was made.f This would tend greatly to the secu- rity of landed property, and perhaps would be the best reme- dy for the variation of the magnetic needle, and for the differ- ence between two compasses which differ, that can be invent- ed. 0^' PRACTICAL S^SVEYI^*G. It would be no easy matter to describe all the ditferent me- thods which may be employed in different cases, in taking the field-work of a survey. Only one case will be given here, which is represented bv the following figure. See Fig. 1. Fig, 1. The survey was be- gun at the corner num- ^ 7n 2 bered 1. The corner numbered 2 was in a pond. The course and distance were taken / ""-{7^ from 1 to ?7i, then from m to n. The angle at 2 was righl, of course there w^as a right an- gled triangle, wherein the angles and hypoth- enuse were given, to find the sides m2 and \ / _.,0 2n. From n to 3, the ^'-'--.^^^ "^ ^.^"^ course and distance *^*-- »-_---'^' were taken on the line. * In proportion as the value of land increases the use of the compass in surveying wiU be probably abandoned. It is, at the present time en- tirely laid aside in the accurate surveys in England ; and though lines may be more expeditiously run with a compass than otherwise, yet the other mode may be employed, under all circumstances and with far ->a greater accuracy. — Ed. t There is some obscurity here in the author's phraseology. He APPENDIX. 80 The next line ran through a thicket in a swamp, where noth- ing could be done correctly. Courses and distances were taken from 3 to s, thence to z, thence to 3, and the course and distance of the line 3 — 4 were calculated by u traverse from those courses and distances. t At the angle 5, a tree stood on a high bluff of ledges, inaccessible on either line ter- minating at that point. The course from 4 to 5 was taken at 4. Next, the course and distance were taken from 4 to a, and from a the course was taken to 5. Next, the course and distance were taken from a to 6, and from 6 the course was taken to 5. Two oblique triangles, with the angles and one side in each, were given to find the sides 4 — 5 and 5 — 6.* The closing hne ran through thick bushes and water, and the course and distance were taken on the dotted line to the line 1 — 2, at a point twenty rods from 1. The course and dis- tance of 6 — 1 were calculated accordingly. Whenever a line runs through or over a place where it is difficult to take either course or distance correctly, if, by ta- king a traverse around at a little distance, the surv eyor can have level, clear land, and then calculate his course and dis- tance by the traverse, he will be more likely to ascertain the true course and distance than by continuing on the line. Directions for running lines* Many people suppose that a surveyor at the beginning of a line, by intuition or some magic art, can set his compass di- rectly to the terminating point, whatever obstructions may in- tervene, and that he needs no assistance ; but this a mistaken idea. In running a line of considerable length, a surveyor should have two assistants to carry the chain, and two to car- ry flags, in whose ability and correctness he can confide, and a fifth to use an axe. If the surveyor is not furnished with such a set of assistants, his employer need not place too much confidence in his work. The flag staves should be as much as two and a half inches in diameter, or what would be better, probably means, placing his compass on the same meridian, observing the variation, and making alloivance for the change in the direction of theneedle, since the preceding survey. — Ed. * If the point 5, is on an elevation, it is evident that the lines 4 5, and 5 6, will not be the required distances, but will be each a hypothe- nuse in a right angled triangle, of which the required distance is the base. — Ed. t The line 4 3 may be found in the same manner as, CI, page 75, ex. 11.^^. 68.-ED, 90 APPENDIX. two stripes of a board of that width and seven or eight feet in length. If they are not so wide they cannot be seen through the sights of the compass at any great distance. On one end of each staff, a red flag of a yard in length should be wound tight, and not left to hang loose and flutter in the wind. Red will be more easily seen through bushes than any colour, and the brighter the colour the better. Being thus manned and equipped at the beginning of the line, he must set his com- pass as near the true line as he can, or, what would be better, he may set up one of the flags at the place of beginning, and go forward as far as he can have a fair view of the back flag, there set his compass on his random line, and send the other assistant as far forward as he can conveniently see the flag. When each flag is clearly seen through the sights of the com- pass, the back flag must be brought up and placed where the compass stood. In this manner he must proceed on his ran- dom line, taking care each time he sets his compass to turn the sights to the back flag. Great care must be taken to keep these flags perpendicular ; also the surveyor must keep the stafl* and the sights of his compass perpendicular. A little leaning of the flags, or turning the sights of the compass from a perpendicular, will make a crooked line. In looking through the sights of the compass to the flags, the surveyor must look as near the ground as he can, and, when practica- ble, the flag should be turned down, on account of the danger of being leaned when kept up. All obstructions, such as bushes, brush, &;c. must be clear- ed away. The random hne must be measured, and at con- venient distances, perhaps at every twenty rods, stakes must be set directly in it. Every stake must be numbered, that no mistake may be made in calculating, when they are after- wards removed and placed on the true line. If, in the course of the random line, the magnetic needle does not traverse as at first, or traverse ahke at different places, no regard must be paid to it — the two flags must direct the course ; neither should the surveyor be turned aside or terrified by the cry of either of the parties, you are wrong, you are wrong, (for he will most certainly hear it,) but he must continue his random line, until turning at right angles, either to the right or to the left, as the case may be, he can exactly strike the bound, or the point where a bound is to be erected ; there he may stop, and measure the distance from that place to the bound. Then, havmg the length of the random line, and the distance from its termination to the true bound, he has the legs of a right angled triangle, the hypothenuse of which will be the length of the true line ; also the angle contained between the true and the random line must be added to or APPENDIX. 91 subtracted from the course of the random line, (as the case may happen,) which will give the course of the true line. Suppose the whole length of the random line is 200 rods, and the distance from the termination of it to the bound is 90 links, the calculation for setting the stakes on the true line may be made thus : — As the whole distance is to 90 links, so is the distance of any stake, to the distance that such stake is to be moved. If the stakes are 20 rods apart, the answer is, the first stake is to be moved nine links, the second 18 links^ and so on, adding 9 links at each stake, until the whole are moved at right angles from the random to the true line. Most of the crooked lines, and consequent disputes and law-suits between farmers have arisen from the want of this care and attention. When a long line is to be run over a number of ridges and through intervening vallies, it should first be run and estab- lished from one ridge to another, and the intermediate spaces in the vallies may be taken afterward. By taking long sights there will be less danger of turning from a straight line. In all cases, the forward flag should be carried as far as it can be distinctly seen, unless it is at the termination of a line. ON KEEPING UP BOUNDS. As the magnetic needle cannot be relied on in renewing lost boundaries, it is of the first importance that good, substan- tial bounds be made and kept up. In divisions, or distribu- tions of lands, every surveyor ought to see that such bounds are erected. It is his business to see them made, and such bounds ought to be described in deeds, or in the instruments by which the lands are conveyed, and to be made a part of the record. By proper care and attention to this part of the business, an almost endless train of disputes maybe prevented. Highways are attended with more difficulties of this kind than the location of the divisions of real estate. In laying hi o-h- ways, it is the custom to lay the centre lines, and order the roads to be of a certain width. In taking surveys of roads, stakes are usually set at the angles. When the roads are made, all these stakes are lost, and the travelling path is often built on one side of the centre ; but as the bounds are lost, it is utter- ly impossible, after a few years have elapsed, to tell where the road was laid. Surveyors who are employed on such business ought to describe the angles, or as many as is practicable, in such a manner that the road may afterwards be found. 92 APPENDIX. THE FOLLOWING SURVEY OF A ROAD MAY SERVE AS AN EX- AMPLE. Beginning at a point on the centre of an old road, (here describe what road,) 14 rods westerly of the range of the west end of J. T.'s house, thence running S. 17^ E. 84 rods 10 links, to a point bearing west, 54 links from the S. W. corner of a large rock ; thence S. 5° E. 77^^ rods, to a point 77 links east of the centre of a large white-oak tree ; thence S. 7° 3(V W. 67 rods 20 links, to a point bearing west 7 rods 10 links, from a perpendicular crevice in a rock. Enough of the survey is given for the purpose. DIRECTIONS FOR USING THE COMPASS, AND CONCERNING ATTRACTIONS OF THE NEEDLE. In all cases, the surveyor ought to set his compass at least twice on each line, even if he has a fair view of the whole length of it. When there are local attractions, and no two places are found on the same line where the compass has the same traverse, the surveyor should take a medium course, and enter it in his field book, noting such courses, as he may still have occasion to coiTect them in his calculations. If in such cases he is at a loss what course to enter in his field book, and suspects that some minutes may be added to, or subtracted from the course he enters in his book, let him prefix to such courses the sign of addition or subtraction as the case may be, and this will often assist him in balancing his surveys. CONCERNING DRAWING A MAP OF A FIELD. When a map is to be made of a multangular piece of land, whether a calculation or division is to be made from it, the surveyor should measure across the lot in some central place at least once, and in more places if convenient, and the case may require it. By cross measures, the map will be made more correct. The surveyor should not be atraid of wearing his chain by measuring too much. When a survey is to be calculated by plotting, it should not be laid on a scale less than ten rods to an inch. REMARKS ON BALANCING A SURVEY. In every survey which is accurate, the sum of the north- ings will equal that of the southings, and the sum of the east- ings, that of the westings ; but this is not always an infallible proof that the survey is aocurate, for two errors may be com. APPENDIX. 93 mitted, one exactly to balance the other, which no rule will detect ; but such cases do not often occur. In a survey of one hundred acres, whatever may be the number of the an- gles, the difference between the two columns of latitude and those of departure, ought not to exceed a rod for each, but to come within these limits if possible. If in such a survey either of the differences should exceed a rod, where the land is valuable and easily surveyed, it would be better to take a re-survey, at least, so far as to de- tect the error. Some authors have given rules for balancing surveys, which are indiscriminately applied to every line in the sur- vey, which presupposes that a proportional error must have been committed on each and all, both in courses and distan- ces, when in almost every survey, a part of the lines are on land so level and so clear from obstructions of any kind, that if the surveyor and chainmen attend to their business, they will not be likely to commit much error on them ; while other hnes on other parts of the same survey are attended with so many difficulties, that when they have done their best, it will scarcely be possible for them to avoid some error, and the surveyor who takes the survey will best judge on what lines the errors were committed, and whether they are in the cours- es or in the distances. In all cases the corrections should be made on the lines containing the errors. When the er- rors are in the courses they should be corrected, and when the errors are in the distances, the correction should be in them : or the corrections may be in both courses and dis- tances as the surveyor may judge proper. When a course is not directly north and south , or east and west, if the correction of it increases the latitude and dimin- ishes the departure, or if it diminishes the latitude and in- creases the departure, so as to bring the differences to an even balance, it is good evidence that the course contains some error. On EECTANOrLAE SUBVEYING, Rectangular surveying is a name given to the method here treated of, by the late governor Treadwell. A more appropriate name could not have been given ; for the whole survey is reduced to right angled figures, such as triangles, trapezoids, squares, and rectangles. The operation APPEM)IX from amendian from wii t ralcnlated. The caladatioiis are i. lan dravn, eidier at die eaateni or atthe v is^i ^ :rziiiTof the m^. All the spaces lying betwei 'r'A the mei^ian from wliicii tiie sorrey is eaic ^ t en the paraUds erf latitiideoftlieiioitliem £: - ri^ies ofit,areiD. eluded in the eaknlalici : e are drawn from each ai^^ to oie Zii^ncaaiL, p-^dCii ^e called In finmmg the colomn <^meiidian distanoes, vfa^i the ; ndian is drawn at the eastern estremdty, the westings are ad- ded and die eastings are sabtracted. When the nieii£an is drawn at the western extrendtj, the eastings are added, and the westingiB are sobtracted. The meii£an dfetanees |»oeeedi2]g from each end (^ahne, are added together, to form the c«dmim oi doobie mean dis- mneesyidni^thecniipilerof the mr^oii^ woik has eaDed second depaitnre eafamu. The wb^e is iDnstiated by die fi^wing figure. SeeF^.2, APPENDIX. 95 Directions for calculating meridian distances by several me- thods ; ALSO for plotting a survey from the several latitudes and meridian distances, without the use of the protractor, or the line of chords. o rf) -* M u^ Tf iO •<^ •rf* r- lO lo o o OS CO I— I CO _U0_ CO ^ 3 IS CO M r-< CO GO -J CD GO T-i GO CO I O) GO ' &< ' ^ o ,8 CO W H 25 ^ T^ I CM" H ^ ^ ^ s § s o lo s M 1 ai 02 I GO I ^ j iC I CO I to -^ GO U5 O I lO GO C I GO 05 CO ffjGO 96 -\PPEM)IX. Fig, 2, Mendisn Dis- tances, and dou- ble mean distan- ces,* are more proper terms or names for the eishth. and ninth columns, than first departure, and second de- parture. The meaning of the term me- ridian distance, is the distance made firom any meridian. It is not Tery essen- tial by what names the col- umns are called, as names have no effect on the final result. This survey is calculated firom the meridian of the station. To form the first column, marked at the top Mcrid. Dist. ^t the easting 16.90, against the first station into the col- umn, which is the meridian distance of 2, or the distance firom 2 to ^ ; to this mmdier add the next easting, and they make 22.11, the meridian di^ance of 3 ; to this number add the next easting; and they make 80.07, the meridian distance of 4 ; firom this numb^* sabcraet the first westing, and 73.82 jremains, the mesidian distance of 5 : from this number, sub- tiael ihe next wei^iB^ and 70. S3 remains, the meridian dis- tance of 6, or the wesdng of the closing hne. Subtract the last westingx and OOuOO reoBains. Next, form the column of dodUe mean dBsfaaees hy adding two opposite sides of the differeiA figures. Set the first Merid. Dist. into the column. To the first meridian distance add the second, and they make 39.01, the double of the figure 2S/«.t To the second, add nrst APPENDIX- 97 the third, and they make 102.18, the double of the figure 64mn. To the third, add the fourth, and they make 153.89, the double of the figure 45am. To the fourth add the fifth, and they make 144.15, the double of the figure 56az. To the fifth add the sixth, and they make 70.33. The second column, marked at the top Merid. dist. is com- monly called the Pennsylvania method. Only one column is used in finding the meridian distances, but the operation and final results are the same as when two columns are used. This method is not so easily explained to the learner, but is perhaps preferable in practice, because an error may be com- mitted in forming the column of double mean distances, which may not be discovered, but in this method, an error cannot be committed without being detected. To form this column, set the first easting, 16.90, in the up. per place, and add it to itself, and they make 33.80 ; to this number, add the next easting, and they make 39.01 ; add the same easting again, and they make 44.22; to this number add the last easting, and they make 102.18 ; add the same easting again, and they make 160.14 ; from this number, sub- tract the first westing, and 153.89 remains ; subtract the same westing again, and 147*64 remains ; from this number subtract the second westing, and 144.15 remains ; subtract the same westing again, and 140.66 remains ; from this num. ber subtract the last westing, and 70.33 remains ; subtract the same westincr aorciin, and 00.00 remains.* * The demonstration of this method is not given above : and as it may be of assistance to the surveyor in many cases, it is here inserted. The first multiplier, (or first number in the column of double mean distances,) is the same as in the common mode, because in both cases, it is the first easting. This, in the figure, is s2. Now the next multi- plier ought to consist of ^2, and n3, added together. The line n2 con- sists of the first two eastings. Therefore the second multiplier ought to contain twice the first easting, and once the second. By the method above, the first easting is doubled, but is not used as a multiplier. But, by adding the second easting to this double of the first, the second mul- tiplier is obtained, and set down accordingly. To this multiplier, if the same (second) easting be added, it will make the line s2 equal to ?a3, and the number will then be twice n3, which is set down, but not used as a multiplier. The third multiplier ought to consist of n3 and m4. The line m4 is greater than the line n3, by the third easting, and, of course, the third multiplier ought to be twice r?3, together with that easting. To the last number set down, then, (which was twice n3), add the third easting, and the third mul- tiplier is found. To this multiplier, if the same easting be again added, it will in- crease the fine ?j3, to m4, and the number will then be twice m4, which is set down, but not used as a multiplier. The next multiplier ought to consist of m4 and a5. The line a5 is less than m4 by the first west- 12 98 APPENDIX. The upper numbers in this column are the same as the double mean distances which stand against them. For the remainder of the process in finding the areas, pro- ceed as before taught in this work. The north area against the first station is the double of the triangle 125 ; that against the second, is the double of the fig- ure 2Sns ; that against the third, is the double of the figure 24:77111 ; the south area against the fourth station, is the double of the figure 4Dam ; that against the fifth is the double of the figure 5Qza ; that against the sixth, is the double of the tri- angle 6U. The three north areas all lie without the field, and are bounded north on the line ??i4. The three south areas con- tain all within, and all w-ithout the field, which is included in the calculation. It is obvious then that Avhen the less is sub- tracted from the greater, the contents of the field ^nll remain. Another column maybe formed as the eleventh in this ex- ample, which, for distinction, is here called half departure. It contains half the sum of the numbers in the double mean column. These numbers when multiplied by their respect- ive northings or southings, give the simple areas of the differ- ent figures. This method is preferable in practice, as the multiplications are greatly diminished. When the last deci- mal in the double mean distance is an odd number, a unit may be taken off, and take half the remainder, rather than annex another decimal : perhaps this would not make the difference of a rod in a survey of one hundred acres. Or the odd numbers in the last place of decimals may be balanced by sometimes adding a unit. If the numbers are diminished a trifle, it may be remarked, that, on account of the uneven ing, and, of course, the fourth multiplier ought to be twice m4, dimin- ished by that westing. From the last number, then, (which was twice wi 4, take the first westing, and the remainder will be the fourth multi- plier. From this "multiplier, the same westing being taken, the line mA v.'ill be dimmished to a5, and the number will then be twice a 5, which is set down, but not used as a multiplier. The fifth multiplier should consist of a5 and s6. The line s6 is less than a5 by the second west- ing, and, of course, the fifth multiplier should be twice a5^ diminished by that westing. From the last number, then, (which was twice a 5.) take the second westing, and the fifth multiplier is found. From this multiplier, the same westing being taken, a5 will be di- minished to £6, and the number will become twice £6, which is set down, but not used as a multiplier. The final multiplier should be z6 alone, since its area, lz6 is a triangle. The final westing is ^6, which taken from the last number, (which was twice ;i6,) leaves s6 for the final multiplier. A clear understandmg of the theory of this method, will be a greai assistance in performing the practical operations.— En. APPENDIX. 99 surfaces, there is danger of making the distances too much, rather than falUng short of the true measure. To PLOT THE FOREGOING FIELD FROM THE SEVERAL LATI- TUDES AND MERIDIAN DISTANCES, WITHOUT THE USE OF THE PROTRACTOR, OR THE LINE OF CHORDS. First, set the northing of the first line from 1 to 5 ; set the northing of the second Hne from s to n; set the northing of the third Hne from ntom; set the southing of the fourth line from m to a ; set the southing of the fifth line from a to z; next, from these points, draw parallels of latitude perpendi- cular to the meridian ; then, on these parallels of latitude, set the meridian distances of the several stations, from s to 2, 16.90 ; from n to 3, 22.11 ; from m to 4, 80.07 ; from a to 5, 73.82 ; from z to 6, 70.33. From one of these last points to another, draw the boundary lines of the field, and if the plan does not perfectly close, it is because some error was com- mitted in the process, or in the field, or the scale was incor- rect. In practical surveying, it is next to an impossibility in any case, to work so accurately that the survey will exactly close without some correction. The difference between the two columns of latitude, and the two columns of departure, are the legs of a right angled triangle, the hypothenuse of which will be the distance which the survey will fail of closing. These diflEerences, as before taught in this work, must be balanced, and the column of meridian distances must be form- ed by the numbers as balanced. When the survey is balan- ced, and this method of plotting is taken, the parallels of lati- tude must be laid down according to the balancing, and the map will perfectly close.* When the courses and distances are corrected according to the balancing, they will form a survey which will contain no error. N. B. Great care must bo taken to keep the latitudes par- allel and perpendicular to the meridian. The better to effect this, a meridian line may be laid on each side of a sheet, or a *^ This language is not clear. If it be meant that the sides of the field are to be drawn from point to point, as marked on the parallels, which is the usual method of plotting from a meridian, one survey will close as perfectly as another. But if it be meant, that they are to be laid down from these points, according to the courses and distances in the field book, then it is "by no means certain that the map will close, and, on the other hand, is rather probable that it will not, if, in balan- cing, there was any great error to be corrected. It is only after tha courses and distances have been corrected from the balanced latitudes and departures, that a map plotted as above can be expected to corres- pond with them. — £i>. 100 APPENDIX. half sheet of paper, as occasion may require, and the mea- surements made on both sides. The following survey is calculated fro3i a meridian running through the map ; of course, a part of the me- RIDIAN DISTANCES ARE EAST, AND A PART ARE WEST. See Fig. 3. Fig.Z. 1 ^ m 7/ /-^^^ ,^^--^^ 'z \ ^^ ^^-^^^^ r ^ \ \ i — ,•— ^ — - — ^j- n \^ § ^ ^ e a: no' Courses, ^^f]' 1 iKOQ N. js. 1 E. vv. i i \ 1N60°00'E 20.00 ! I 10.00 17.32 17.32 34.64 54.64 74.64 E. E. E. E. 173.20 1 2 S.30 OOE 40.00 i i ■34.64 1 20.00 1892.73 3S70 00W70.00 1 \ 23. 94 ■^-'■^^^% E. W w w 212.10 1 4N3000W40.00 1 1 34.64 13.46 -■^p, 2664.50 ! 5N.7400E50.42 I3.9J \ 18.46 )0.00 w 675.53 173.2015444.86 173.20 2)5271. A. R. R. 160)2635(16 1 35 160 1035 APPENDIX. 101 The column of meridian distances in this example is formed by adding twice, or subtracting twice against each station, as in the Pennsylvania method. Set the first easting in the up- per place, which is the distance from a to 2, being east me- ridian distance ; add it to itself, and it makes 34.64 ; to this number add the next easting, and they make 54.64, east me- ridian distance from a to m ; add the same easting again, and they make 74.64 ; from this number subtract the first westing, and there remains 8.86 east meridian distance from i to s. As the first westing cannot be subtracted again, the last east meridian distance, 8.86, must be subtracted from the first westing ; this crosses the meridian, and gives 56.92 west me- ridian distance in the lower place. Having crossed the me- ridian, the westings must now be added, and the eastings subtracted. To the 56.92 in the lower place, add the last westing, and they make 76.92 west meridian distance from r to w ; add the same westing again, and they make 96.92 ; from this number, subtract the easting of the closing line, and there remains 48.46 west meridian distance, from -y to 1, or the easting of the closing line : subtract again, and 00.00 remains. Hav- ing completed the column of meridian distances, next multi- ply the upper number against each station, by its northing or southing, and set the products on the east side of the meridian, in their respective columns of north or south areas ; but on the west side of the meridian, the order is reversed ; the north products are set in the column of south areas, and the south products are set in the column of north areas. The north area against the first station, is the figure 2z\a ; the south area against the second station is the figure mnia ; the south area agamst the third station, is the figure sxie ; the south area against the fourth station, is the figure uwer, made by the northing of the fourth line ; the south area against the last station, is the figure uSrl.* * In this survey, the learner, without farther explanation, would be liable to meet with some perplexity. This will be particularly the case, where the meridian is crossed. In the diagram, the double areas are represented in full. The first is a north area \a2z^ which is double of the triangle la2. In this, the multiplier is a2. The next multiplier should consist of a2 and ?3, which is found by doubling a2, and adding to it the next easting. The corresponding area, amni^vn. ay be seen to be double of a23i, for if 23nm were to be turned about, and laid on a23z, it would exactly cover it. The next step is to add the same easting to this multiplier, (viz. a2 added to t3 ;) and as this increases the a2 to z'3, the sum is twice i3. From this number (twice i%) the first westing is to be taken. If this westing extended no farther than the meridian, it would be just i3^ and on subtracting this from the twice i3, we should have once i3 lefl. 102 APPENDIX. The foregoing columns of meridian distances might have been commenced, by setting the first easting in the lower place, and the additions and subtractions, made as before directed, and the last subtraction would end in 00.00 at the upper place, against the first station. In this case, as there would be no upper number against the first station, there would be no product in either column of areas against it. The east meridian distance against the second station would extend no further east than the third station, and the meridian distance against the third station, would be on the west side of the meridian ; and the meridian distemces, against the fourth and fifth stations, would extend as much farther west, as the easting of the first line. But it goes beyond the meridian, to a distance, e4. The distance e4, must therefore be likewise taken away, leaving not once iS, but i3 di- minished by e4. In the figure, a distance, 3^, is cut off from i3, equal to e4, leaving is, which is what remains after the first westing is subtract- ed, and constitutes the next multiplier. This, multiplied by ze, its southing, gives the area eisx, which is double of ighs, as will be seen from the following. 35 being equal to 4e, and the triangles 3sh, and 4eg, being similar, co- is evidently equal to sh. And 3i being equal to 4a;, and the triangles Sig and 4xh, being similar, ig is equal to hx. Then if the figure ighs were to be turned about and placed on the figure eghx, it would exactly cover it, and of course must be equal to it. The area eisx, then, is double of ighs, which is the dilFeronce between the triangles Sig and Ssh, or 'ieg. This area, therefore omits the part of the field, Ssh, and there is no other area which includes it. But the next area, eruic, in- cludes its equal, Aeg, which is not a part of the field, and thus restores to the field its full contents. The reason why the south areas, after crossing the meridian, are written in the north column, and north, in the south column, is made clearer by the following illustration, than by any other method. ^ Suppose that the part of the above dia- gram, 1, 5, 4, 0-, be made to revolve about g as a hinge, until the point 1, is directly ^ south of 0-, and the line Ig forms a straight ^ line with ga ; as in this figure. The areas in the figure ^§'451, being brought on the east side of the meridian, now be- 7"" come south, and must, of course, be pla- ced in the south area column. But before the revolution, the same areas, being on the west of the meridian, were north. Hence, when a survey is calculated from ^ meridian passing through the field, north areas on the west side must be treated like south areas on the east, and vice versa. It will be ob- served, that, after the revolution, instead of the area eisx, we have the area eis'x'-, which may easily be shown to be equal to the former. — Ed. APPENDIX. 103 The products against the second, fourth and fifth stations, would be set in the cohimn of south areas, and that against the third station, on account of its being on the west side of the meridian, would be placed in the column of north areas, and would be subtracted from the footmg of the south areas. When a survey is calculated from a meridian runnmg through the map, it is always best to set the first departure in the lower place, as it saves one multiplication. On distributing estates, A farm is to be distributed among a number of heirs. A survey is made, and the difference, between the columns of la- titude, and between those of departure, is two rods for each. The survey is balanced, and calculated arithmetically, and is found to contain two hundred acres. The surveyor next .draws his map, by which the divisions are to be made, ac- cording to the courses and distances. The plan does not close by nearly two rods and three quarters. He next cor- rects the lines, and makes the map close as well as he can ; and when the divisions are made, they may not agree with the first calculation, by two or three acres, or more. Should the map be drawn as before directed, by the meridian distan- ces and the latitudes as balanced, it would close, and would be in exact conformity to the calculation made arithmetically. If the divisions are made arithmetically, without the use of the scale and dividers, the calculations must be made accord- ing to the balancing, or the divisions will not agree with the first calculation. It will be acknowledged by every experienced surveyor, that it is a difficult matter to make the amount of a considera- ble number of divisions agree with the whole, when calcula- ted by itself. It is the common practice in distributions, to make the di- visions with scale and dividers ; this method will answer well provided the map is drawn on a large scale. The following is a useful rule in dividing lands, when any quantity is to be added to, or taken from, a division in the form of a triangle. Having the area, the contained angle, and one side of a triangle given, to find the adjoining side, including the an- gle. 104 APPENDIX. Rule. To the sine of the given angle, or of its supplement if obtuse, add the logarithm of the given sida; subtract radius from this sum, and subtract the remainder from the logarithm of the double area, the last remainder will be the logarithm of the side required.* In taking a survey, go around with the sun, not that you can work more correctly, or that it will have any effect in calculating, but when you put your courses and distances on your map they will follow around from the left to the right, and thus render the plotting easier. Wherever you begin, set your compass on the angle and cause a stake or a flag-staff to be erected at the next. When your line runs over a hill, cause a stake to be erected at each end of it, and take your station on the top of the hill, directly between them. If bushes obstruct the sight, make an offset, or set your compass a little distance from the line, from whence you may see the back flag, and cause the forward flag or stake to be set opposite the bound in a direction with the compass and the back flag. When the line is measured, measure the distance from the flag to the bound, and calcu- late your true course by trigonometry. If your next line is of such a distance that you cannot see through the whole length of it, run as near the true line as you can, and if you do not exactly strike the bound, measure the distance from the termination of 3'our random line, and calculate your course as before directed, or if you can discover a tree stand- ing near the termination of yoiir line, take the course and dis- tance to that, thence to the bound, and calculate your true course and distance. By practice and experience, a method for taking courses will soon become familiar, in all cases. In measuring hills and inclined surfaces, the horizontal distances must be taken. A plummet should be suspended from the end of the chain, when it is levelled. Where hills are very steep, the survey- or should assist the chainmen, and when the best is done in levelling and plumbing the chain, judgment must frequently be called into exercise. Even when rises and descents are easy, there is danger of making too much measure. In such cases, chainmen often make allowances, but the surveyor would do better to keep them to close measure, and from the shape of the ground judge himself what allowances ought to be made. If he is experienced in his business, he will form a more correct judgment than inexperienced chainmen. Par. ticular care must be taken that the chain is carried on a ♦ This is a repetition of the rule on page 78.— Ed. APPENDIX. 105 straight line, and that it is well straightened. When B. tally is ended, and the hinder chainmen brings up the sticks, they must be counted. When on counting the sticks it is discovered that one is lost, the chainmen should not leave the chain and go back to find it, but, from the last mark, should measure back to the point where the tally began, to see whether one chain is lost from their measure.* Many blunders in this way have been left undetected by not taking this care. A careful accurate chainman never lost a stick or mis- counted a tally. Young surveyors should practice much for their own instruction, and should make correct practice fa- miliar before they offer their services. It is as necessary that they should spend some time in acquiring a practical knowl- edge, as it is that they should spend any time in acquiring a knowledge of theory. A young surveyor should bear in mind that if he is detected in one error in the beginning of his practice, it will be more to his disadvantage than to be detected in two when he shall be well established. If an error is committed in a survey, it is not against the surveyor provided he detects and corrects it, but if he cannot detect and correct his own errors, that is suf- ficient evidence of his deficiency in point of knowledge and skill. 1. N. 250 00' 2. N. 10 00 3. N. 75 00 4. S. 10 00 5. s. 5 00 6. s. 85 05 Form of a field book. Beginning at a merestone at the southwest corner. Rods Links E. 40 00 to a white-oak tree, E. 30 00 to a heap of stones, E. 60 00 to a maple tree, W. 36 00 to a pine tree, W. 40 00 to a spruce tree, W. 70 12 to the place of beginning. When a survey is calculated by chains and links, the num- bers are less than when it is calculated by rods and decimal parts. Every method by which the numbers are diminished is an improvement. In a hilly country, the two-pole chain is preferable and is more commonly used, because it can be levelled better. Hills are often found so steep that even the two pole chain cannot be levelled. * Or to see whether the backward measurement brings them, with the sticks they have, to the place where the tally commenced. — Ed. K 106 APPENDIX. MlSCELLA^TJOUS. When a survey is calculated by chains and links, and the contents stand in acres and decimal parts of an acre, it may be multiplied by the price of an acre, and the product will be the amount. Example. A piece of land, 12 chains and 25 links m length, and 10 chains and 25 links in breadth, is sold for 820 25, per acre ; — what is the price of it ? Length 12.25 Breadth 10.25 6125 2450 1225 Acres and decimal parts 12.55625 Price of an acre 20.25 627S125 2511250 2511250 N. 44 W. s. rv E. S. 25 E. Answer 8254,26.40625 The wTiter know^s not w^ho invented the following rules for finding contained angles. For plainness, they are not ex- ceeded.* N fi2= F ) When the first letters are alike, and the two ^T* A A T»T* > last are unlike, add the degrees of both conrses ^ together, which gives the contained angle. \ When the two first and the two last letters are V alike, subtract one course from the other, and J the remainder will be the contained angle. "J When the two first letters are unlike, and the N. 64° E. ! two last alike, add both courses together, and S. 35 E. j subtract their sum from ISO. the remainder will J be the contained angle. ^ When the two first and the two last letters N. 57° W. ! are unlike, subtract one course from the other, S. 25 E. j the remainder from 180, and the remainder will J be the contained angle. * These rules are nothing drSerent in principle, from the common rules, ^ao-e 50, and, in their practical application, by no means as sim- ple. To one who understands the theory of the common rules, they are the most simple, which can be invented ; and to one who does not, the rules above will be still more difficult of comprehension. — The re- APPENDIX. 107 Application of the above rules. Two courses are given, viz. N. 67^ W. and 28° E. to find the angle. — Suppose yourself standing at the point where these courses meet. Reverse the letters of the first course, and they will stand thus, S. 67° E. > The third rule apphes in N. 28 E. \ this case. When the quantity of any angle in a survey is wanted, the preceding course must be reversed ; then both courses will run from the same point. versing of the letters of the first course is troublesome and perplexing. Perhaps, however, for practical men, the common rules may be improv- ed in some degree, by expressing them as follows. I. If the first letters are alike, and the last also, add thb LESS course to the SUPPLEMENT OF THE GREATER. II. If THE FIRST LETTERS ARE ALIKE, AND THE LAST UNLIKE, SUBTRACT THE SUM OF THE COURSES FROM 180°. III. If THE FIRST LETTERS ARE UNLIKE, AND THE LAST ALIKE, ADD THE COURSES. IV. If THE FIRST LETTERS ARE UNLIKE, AND THE LAST ALSO, SUB- TRACT THE LESS COURSE FROM THE GREATER. In employing these rules, the letters may be taken as they stand in the FIELD BOOK. A sct of figures like the following well fixed in the mind, will be a great assistance to the learner. Rule I. Rule IL N. 20° E. N. 70 E. N. 50^ E. N. 40 W. 108 APPENDIX. CONVERGING OF MERIDIA.NS. The length of a degree of longitude in any parallel of lati- tude is to the length of a degree upon the equator, as the co-sine of that latitude is to radius. R. : 60 miles* : : co-sine of the lat. : the length of a degree on that lat. Rule III. Rule IV N. 259. E. S. 60 E. N. 82= E. S. 35 W. Tsri It will be seen that the required angle, in each case, is ABC. A set of figures of this kind, once fully understood, and fixed in the memory, will be the best means of rendering this subject simple. We recom- mend to all learners, to study the above with attention. — Ed. "^ This proportion is for geographical miles or minutes of a great cir- cle of tlie earth. Of course, to the practical man, it is of little use. For statute miles we should employ, instead of 60, the number of sta- tute miles in a degree. This number has been commonly laid down at 69i. This estimate is, however, undoubtedly too great. It is, not- withstanding, difficult to assign the true length of a degree, when our measures themselves are liable to change. Until some universal and permanent standard of length shall be adopted throughout the country, we shall hardly be able to speak with much certainty on this subject. The ten millionth of a quadrant of a meridian of the earth has been adopted for a standard in France. In England, and of late years in the state New York, the pendulum has been made the regulator of measures of length. In modern English measure, a degree is but little more than 692^ miles, acccording to the measurements most relied on. When it is recollected that between the various measurements, which have been made, of degrees on the earth's surface, there have been re- markable differences ; that in different parts of the w^orld, the degrees vary in length, increasing always from the equator to the poles ; and that a very trifling variation in smaller measures, as a foot, or yard, may become very perceptible in a distance of 60 or 70 miles, the diffi- culty of assigning the length of a degree accurately, will be perceived. APPENDIX. 109 As radius Is to 60 miles, So is co-sine lat. To 30 miles 10.000000 1.778151 9.698970 11.477121 10.000000 1.477121 d,: CL \h the size of your Through h, the TO CHANGE A MAP PROM ONE SCALE TO ANOTHER.'*' Fig. 4. Suppose the map to be ABCD. It is desired to draw a larger map of the „-''' same field, without the necessity of plotting a- gain. Take any point within the field, as E. From this point draw lines of indefinite length thro' all the angles of the field, A, B, C, and D. Take Ea of such a length that EA : Ea may express the ratio, in which you wish to increase map. Through a draw ah, parallel to AB. point where ah intersects EB extended, draw he, parallel to BC. Through c, the point where he intersects EC extended, draw cd parallel to CD. Through d, the point where cd in- tersects CD extended, draw da, parallel to DA. The line da will intersect EA extended, at the starting point, and abed will be the enlarged map. If it be required to draw a map smaller than the given one, the point a may be taken within the field, and the process will be similar. If the plot, which it is desired to enlarge, be near one side of the sheet, so that it cannot be extended in that direction, At present, it is most generally considered about 69j miles. Consid- ering it as such, the proportion above, will become, R« ; 691 miles : : co-sin. lat. : length of deg. in that lat. If, then, the latitude be 60°, as above, the length of a a degree will be 34f miles. — Ed. * This and the following problems are not contained in previous edi- tions. — Ed. K3 no APPENDIX. the point E may be taken in one side or an^le. And -ene- rallv, it may be observed, that the nearer tiie point E is ta. ken to one side of the map, the less will the enlarcred plot ex- rend in that direction. Thus, in the figure, E is nearest the side AB, and the map extends least onthat side. To FXXD T3.Z AREA OF a FIELD &E03(EETBICALLY. ET EUDF- CiyG IT TO A TELLXGLE. Fi£. 5. In many cases it is convenient to be able to make an esti- mate of the quantity of land in a field, "^th tolerable accuracy, but without the trouble of a tedious computation. In such instances, the plot may ofken be reduced, -ith : rvantage, to a triangle. Let ABCDEF be the field. I observ-e a re-en-erins angle, on the north side, viz. CDE. If I join CE, the plot will con- tain too much, by the triangle CDE. If I, then, cut ofi" a por- tion, equal to CDE, the proper quantity will be left. I draw DG, parallel to EC, and join EG. Since DG is parallel to EC, the height of the triangle EGC, is equal to the height of the triangle CDE. And as they stand on the same base, EC, EGC is equal to CDE ; for the area of each is found by multiplying half the bass into the height. Taking awar EGC, then, there is left the figure ABGEF, equal to the ori- ginal plot, but having one side less. Thus the side EG has been subsrituted for the two sides, ED, DC. In like manner, by joining EB, and drawing a hne fromG to H, parallel to EB, I may substitute EH for the two sides EG, GB. In like manner, also, by joining EA, and drawing APPENDIX. Ill a parallel, FK, I may substitute EK, for EF, FA. The plot has now become a triangle, KEH, whose area may be found geometrically, by moB. IX. rule I. p. 40. It will not be ne- cessary actually to draw the parallels. Let a rule be laid across E to A, for instance, and placing one foot of the divi- ders in F, let the other just touch the edge of the rule. With this distance, describe small arcs from E and A, and laying the rule across, so as just to touch them, mark the point K, where it crosses BA, extended. MISCELLANEOUS QUESTIONS. 1. At a certain point I took the elevation of a tower S^ 15'^ — then measured toward the tower on an angle of depression 7° 333 feet to a level with the base of the tower, when I took the elevation again, 8°. — Required the height of the tower and the distance from the second place of observation to the base ; also how much higher the land was at the place of the first observation, than at the second. Ans. — Height, 99.6feet. Distance required, 708.0 feet. Difference in the height of land 40.58/ee^ 2. Two persons made observations on the altitude of a me- teor, both being on the same side of it, and in a vertical plane passing through it. The distance between their stations was 200 rods, and at one the angle of elevation was 36° 25', at the other 32° 50', and at the last the disk of the meteor subtended an angle of 2'. — Required the distance from the last place of observation, also the height and diameter of it. M. Q. R. Answer.— The distance 5 3 60 Height 3 70 Diameter 18 feet 2 inches. 3. From the top of a steeple 165 feet high, the angle of depression of the nearest bank of a river is 11° 15', that of the opposite bank is 6° 15'. Required the width of the rivear. Ans. 41.13 j'ods. 4. What length of cart-tire will it take to band a wheel 5 feet in diameter ? Ans. 15 feet 8^ inches. 5. A gentleman laid out a garden in a circle, containing one acre, one quarter, and one rod, with a gravelled walk on the outer side of it within the circle, which took up twelve rods of ground. What is the diameter of the circle, and what is the width of the walk ? Ans. the diameter 16 rods. — Width of the walk 4 feet. 112 APPENDIX. 6. Neptune laid out 1,000 square miles of the surface of the sea in a circle, and sold to -^olus all that part of it which lies without a concentric circle of one third of the diameter. What is the diameter, and how much was sold ? Ans. The diameter 85.68 miles. The quantity sold 88^.^2 square miles. 7. A farmer laid out an elliptical orchard, the longest dia- meter of which was 30 rods, and the shortest was 20 rods, and surrounded the same with a wall two feet thick, within the figure. What is the quantity within the wall, and how much is covered by it 1* A. Q. R. Ans. Within the wall 2 3 22 Covered by the wall 9.3 8. From a point in an equilateral triangle, I measured the distances to each corner, and found them 20, 29, and 30 rods. Required the area and the length of the sides, f A. Q. R. Ans, The area 5 1 33 Length of each side 45 9. Required the dimensions of a rectangle containing one acre and a half, bounded by 64 rods of fence. Ans. 12 by 20 rods. 10. The area of a rectangle is five acres one quarter and thirty-five rods, and the diagonal is forty-three rods. Required the length of the sides. Ans. So by 2d rods. 11. Required the dimensions of a rectangle containing twenty-six acres, one quarter and twenty -four rods, when the length exceeds the breadth by fifty-two rods. Ans. 44 by 96 rods. 12. Required the dimensions of a rectangle containing 250 acres-, when the sides are in the proportion of 7 to 3. Ans. iSO.93 by 305^. 13. The state of Connecticut contains a little upwards of 4,828 square miles, or 3,090,000 acres, including rivers, har- bours, creeks, roads, &c. : if this quantity of land is laid in a sauarCj what will be the length of each side ? M. Q. R. Ans. 69 1 75.11 * In finding the area of an ellipse, the product of the two axes, (that is, of the longest and shortest diameters,) must be multiplied by the same number, by which the square of the diameter is multiplied, to find the area of a circje, viz. 0.7854. — Ed. t This may be solved geometrically. LOGARITHMS. liOGARITHMS. Let there be a series of numbers, increasing by a common difference, as for instance, by 1, viz. 0, 1, 2, 3, 4, 5, 6, &c. and another, viz. 1, 10, 100, 1,000, 10,000, 100,000, 1,000,000, &c. increasing by a common multiplier, 10. The former are the loga- rithms of the latter. It will be seeu that 1 is added in the upper series, as often as 10 is made a multiplier in the lower. If two logarithms, then, be added, and the numbers below them multiplied, the sum of ike logarithms will be the logarithm of the product. Thus, if the logs. 1 and 2 be added, and the corresponding numbers, 10 and 100 be multiphed, the sum will be 3, and the product 1,000. These numbers may be seen to correspond to each other, in the two series above ; there, 3 stands over 1,000, and is, of coarse, its logarithm. So, if 2 and 4 be added, and 100 and 10,000 multiplied, the sum will be 6, and the product, 1,000,000, which may be likewise seen above to correspond. Furthermore, if, from a greater logarithm a less be taken, and, at the same time, the number corresponding to the greater be divided by the number corresponding to the less, the remainder will be the logarithm of the quotient. Thus, if from the log. 5, the log. 3 be subtracted, and, at the same time, 100,000, the number corresponding to 5, be divided by 1,000, the number corresponding to 3, the remainder will be 2, and the quotient 100, which may be seen above to correspond to each other. With a set of logarithms, then, calculated, not merely for the num- bers 10, 100, 1000, (fee, but for all numbers whatever, it is plain that we might perform the operations of multiplication and division, by addi- tion and s'db traction only. Such logarithms are calculated and arran- ged in tables for use. By observing the two ranks of numbers at the head of this article, it will be perceived, that the logarithms increase by a constant addition, (of 1,) and the corresponding numbers by a constant multiplication, (by 10,) ; and therefore, that when the logarithms are in arithmetical progression, the numbers are in geometrical progression. On this ac- count, logarithms have been defined to be a series of numbers in arith- metical progression, corresponding to another series in geometrical pro- gression. But it will be seen that the numbers, 10, 100, 1,000, 10,000, &c. are the first, second, third, fourth, &;c. powers of 10, and that their corres- ponding logarithms, 1, 2, 3, 4, &;c. are the indices of these powers. Hence a better definition is, Logarithms of numbers are the indices, expressing the powers TO which a given number must be raised, to produce those num- bers. This " given number" is called the radix, or base, of the system, and may be any number whatever. The number 10, however, is most con- venient, and is therefore employed in the common tables. 2 LOGARITHMS. The logarithm of 1 is 0, and that of le is 1. Hence it is evident, that, for numbers between 1 and 10, the logarithm will be between and I. Of course, it will be a fraction ; and, when placed ia the tables, it is expressed by a decimal. For numbers between 10 and 100, the logarithm is between 1 and 2 ; for numbers from 100 to 1,000, between 2 and 3 ; from 1,000 to 10,000, between 3 and 4, and so on, consisting, of course, in each case, in part of a whole number, and in part of a de- cimal. From the above, it will be sufficiently evident, that The integral (or whole number) part of ant logarithm, is a UXIT LESS THA>- the NUMBER OF INTEGRAL PLACES IN THE CORRES- PONDI>-G NUMBER. Or, IT SHOWS HOW FAR THE HIGHEST FIGURE OF THE NUMBER IS DISTANT FROM THE UNITs' PLACE. For example, - The log. of 5,799 is 3.763353 577.9 is 2.763353 37.99 is 1.763353 5.799 is 0.763353 The INTEGRAL PART OF A LOGARITHM IS CALLED THE INDEX, OR CHARACTERISTIC, OF THAT L0GARITH3I. As this characteristic is always a unit less than the number of inte- gral places in the corresponding number, it is evidentthat when this num- ber has but one integral place, the characteristic will be ; which is the case with the last log. above. If, then, the number be a proper frac- tion, or a decimal, and have, therefore, no integral place, or places, the characteristic of the log. on this principle, ought to heless than nothing. Now, since we cannot diminish nothing., so as to render it less than no- thing., we employ, whenever it is necessary to use logarithms of this kind, a characteristic with a mark over it, thus, y, 2^, -3, j. &c. The mark shows that the characteristic ought to be less than nothing, and the number, over which it is drawn, informs us, how much it should be less than nothing. In all cases, then, where it is necessary to add the logarithm^ we must subtract this characteristic ; and in all cases where it is necessary to subtract the logarithm, we must add the characteristic. For, since adding nothing to a number does not alter it, adding less than nothing ought to diminish it. And, since subtracting nothing from a number does not alter it, subtracting Ze^5 than nothing ou^t to increase it.* It will be seen above, that for every division of the number by 10, (or, every removal of its decimal point towards the left) the character- istic becomes a unit less. * An apology may, perhaps be considered necesoary for the language here employed. The writer would not be thought to advocate the ab- surdity that a number may actually be less than nothing ; but the phrase is so concise and expressive, and notwithstanding its absurdity, conveys to the mind of one unacquainted with the nature of negative quantities, the idea intended, so much more perfectly, than any expla- nation we should here have room to make, could do, that it has been thought advisable to employ it. This treatise is intended for practical men, and not for metaphysicians nor scholars. To those who have at- tended to Algebra, the explanation above will be unnecessary. LOGARITHMS. 3 Since, then, the log. of 5.799 is 0.763353, the log. of .5799 will bo t.763353, of .05799 " 2''^63353, of .005799 " 3.763353, of .0005799 " 4-763353, &e. By observing these logarithms, it will be seen, that The negative characteristic of a logarithm, shows how far THE FIRST significant FIGURE OF ITS CORRESPONDING DECIMAL IS DIS- TANT FROM THE units' PLACE. EXPLANATION OF THE TABLE. When the logarithms of numbers, from 1 upward to any other given number, are calculated, and arranged in a table, they constitute a table of logarithms. Tables of logarithms of great extent have been calcu- lated, but those in common use extend to numbers no higher than 10,000. This is far enough for the purposes of ordinarj'- calculation. In the first column on the left of each page, are arranged the natural numbers, and to distinguish this column from the others, the letter N is placed over it. Opposite these numbers in the next ten columns, are arranged the logarithms. For the first 100 numbers, however, on the first page of the table, there is but a single rov/ of logarithms, opposite each column of numbers, and there are four rows of numbers on the page. TO FIND THE LOGARITHM OF ANY WHOLE NUMBER. If the number be less than 100, look for it in the column headed N, and directly opposite to it, in the column headed Log. will be found its logarithm. If the number be greater than 100, but less than 1,000, find it as before, in the column headed N, and directly opposite, in the column headed 0, will be found its logarithm. It will be seen, that when the first two figures of several successive logarithms are alike, they are omitted in the table, after having been once inserted, and only four figures are retained. When, therefore, there are but four figures in the logarithm opposite the given number, cast the eye up the blank till you find two more, which prefix to those already found. It will likewise be observ-* ed, that for the logarithms of numbers above 100, no characteristic is inserted in the table. But this may easily be supplied, since it is al- ways a unit less than the integral places in the number. For numbers between 100 and 1,000, then, it is 2. Find the logarithm of 868. Opposite this number in the table, are found the figures 8520. Casting the eye up the blank we meet with 93, which we prefix to 8520, making 938520. The characteristic, 2, being then prefixed, we have the complete logarithm, 2.938520. If the number be greater than 1,000, and less than 10,000, find the first three figures in the column, headed N, and the fourth at the head of the page. Then, exactly opposite the first three, and in the column headed by the fourth, will be found the last four figures of the required loga- rithm. To these must be prefixed two others^ found as above, in the column headed 0. That is, if the logarithm on the same line^ in the coluran headed 0, 4 LOGARITHMS. contain six figures, the first two of those must be prefixed. If not, cast the eye up the blank, in search of the proper ones, as before. There is one exception to this rule. In some logarithms, will be seen points or periods occupying the places of figures. When this is the case, ciphers must be written in place of the points, and the tico figures to be prefixed, must be sought in the next lower line^ in the column^ headed 0. Thus, Find the log. of 4,177. Opposite 417, and in the column headed 7, are found the figures 0864. The opposite log. in the column headed 0, has six figures, of which the first two, viz. 62, are to be prefixed to 0864, making 620864. Tlie characteristic being joined, the log. is 3.620864. For 4.143, we find opposite 414, and under 3, the figtires 7315. Here we must look along up the blank in the column, headed 0. for the two figures to be prefixed, which are 61, making the log. 617315, which, with its characteristic, is 3.617315. For 4,366, we find opposite 436, and under 6. the figures . . 84. Here, therefore, we must write ciphers for the periods, thus, 0084, and look in the next lovrer line of the col- umn headed 0. for the two figures to be prefixed : which are 64, mak- ing the log. 640084, which, with its characteristic, is 3.640Ci84, If the number exceed 10,000, find the logarithm of the first four figures as above. By the remaining figures, multiply the number opposite, in the column headed D ; from the right of the product, reject as many figures as the given number has places more than four, and add what is left to the logarithm previously found. This sum will be the log. required. The column, marked D, is a column of difierences : that is, it contains the difierences between each two successive logarithms. In many cases a mental estimate may be made, of what should be added to a log. without the use of this column.* The logarithms of pure or mixed decimal numbers should be taken out as if for whole numbers, care being taken to prefix the proper characteristic, in each case. Of vulgar fractions the logs, may be found by reducing them first to decimals, or by the rule given below, in division. TO FIND THE NUMBER, CORRESPOXDING TO AXT GIVEX LOGARITHM. Find the logarithm next less than that given, in the column headed ; pass the eye to the right, along that horizontal line, into the other col- umns, and you will firid either the log. given, or one very near it ; the first three figures of the corresponding number will then be found op- posite, in the column headed N, and the fourth figure, directly over the log. at the top of the page. The integral places in this number wiU be determined by the characteristic of the log. If this characteristic be 3, aU the places will be integral ; if it be 2, one decimal must be pointed off"; if it be 1. two decimals, Szc. On the other hand, if it be 4, a cipher must be annexed to the number ; if it be 6, two ciphers must be an- nexed, and so on. When the given log. cannot be found in the table, however, the num- ber may be more accurately obtained by the following process. Find in the table the next less log., and take the difference between it and the given one. Make this diff'erence the numerator of a fi-action, and the number opposite in the column headed D, the denominator ; re- duce this fraction to a decimal, which write immediately after the four figures corresponding to the tabular log. used. Afterwards place the decimal point where the characteristic of the given log. may require. Thus, find the number corresponding to 2.954921. The next less tabu- LOGARITHMS. 5 kr log. is .954918, and the difFerence 3. Making this difference the numerator, and 48, the opposite number in the column headed D, the denominator of a fraction, we have JL. This, reduced to a deci- ' 4 8 mal, gives .0625, which, annexed to 9014, the number corresponding to .954918, makes 90140625. Pointing off according to the given char- acteristic, we have 901.40625, the number required. Allowance may often be made in the mind, without the trouble of calculation. MULTIPLICATION BY LOGARITHMS. From the nature of logarithms, as above explained, the reason of the following rule will be obvious. Take from the table the logarithms of the lumbers to be MULTIPLIED, AJND ADD THEM TOGETHER. ThEIR SUJI WILL BE THE LOG- ARITHM OF THE PRODUCT. EXAMPLES. 1. Multiply 29.15 by 9.4635. Log. 29.15=1.464639 Log. 9.4635=0.976052 Product, 275.86139-f =2.440691, sum. When there are negative characteristics, it is best to neglect them entirely in the addition, and afterwards diminish the resulting charac- teristic by their amount. Thus, 2. Multiply 71.32 by .3205. Log. 71.32=1.853211 Log. .3205=T.505828 Sum, neglecting i =2.359039 Log. prod. 22.858=1.359039 INVOLUTION BY LOGARITHMS. A number is involved by multiplying it one or more times into it- self. But a number is multiplied by itself, by adding its log. to itself; that is, a number is raised to the second power, by multiplying its log. by 2. In like manner, a number is raised to the third power, by mul- tiplying its log. by 3, and so on. Hence, to perform involution by loga- rithms, Multiply the logarithm of the number to be involved, by the INDEX OF the power. ThE PRODUCT WILL BE THE LOGARITHM OF THE POWER. EXAMPLES. 1. Involve 2 to the twelfth power. Log. 2=0.301030 Multiply hy 12, index, 12 Power, 4,096=3.612360 L LOGARITHMS. 2. Livolve .00003 to the 9th power. Log. .00003=5.477121 Multiply by 9, index, 9 Log. power=^T.294089. Therefore the power is ,000000000000000000000000000000000000000019683. Herejhere were 4 to carry, which made the negative product, 45, equal to •* i . DrV^ISION BY LOGARITHMS. To divide one number by another, Subtract the logarithm of the divisor from that of the divi- dend. The remainder will be the logarithm of the aUOTIENT. EXAMPLES. 1. Divide 15,625 by 625. Los. 15,625=4.193820 Log. 625=2.795880 Quotient, 25=1.397940 Li case the characteristic of the divisor is negative, it must be ad- ded, instead of being subtracted. Thus, 2. Divide 339 by 0.0807. Log. 339=2.530200 Log. .0807=2.906374 Quotient, 4,201^ nearly=3.623326 In case the characteristic of the dividend is negative, or is less than that of the divisor, it is best to increase it by a number, which will make it so great, that the divisor may be taken from it. After the process of subtraction, the same number should be taken away from the resulting characteristic. The best number for this purpose is 10, or some even number of tens. Thus, 3. Divide 77 by 111. Log. 77=1.886491 ; increased by 10=11.886491 Log. 111= 2.045323 Difference, 9.841168 Quotient, .6937= 1.841168 This gives us the mea^s of finding the log. of a vulgar fraction; since a fraction merely indicates the division of its numerator by its denominator. The rule seems to be : Take the log. of the denominator from that of the numera- tor : THE REMAINDER IS THE LOG. OF THE FRACTION. 4. Find the log. of f 4. L02. 25^1.397940; increased by 10=11.397940 Log. 47= 1.672098 Difference, 9.725842 Logarithm required » .725842 LOGARITHMS. 7 \ EVOLUTION BY LOGARITHMS. As evolution is the opposite of involution, its rule must of course be, Divide the log. of the given number, by the number expressing THE root to be found. EXAMPLE. Find the 10th root of 59,049. Log. 59,049=4.771213 Divide by 10=0.477121 Root=3. In the extraction of roots, logarithms will often be found extremely useful. PROPORTION BY LOGARITHMS. Add together the logs, of the second and third terms, and from THE SUM SUBTRACT THE LOG. OF THE FIRST. ThE REMAINDER WILL BE THF LOG. OF THE FOURTH TERM REQUIRED. EXAMPLE. If 23 lbs. of sugar cost |2.76, what cost 250 lbs. .' Statement. 23 lbs. : 250 lbs. : : $2.16 : $ *** Log. 250=2.397940 Log. 2.76=0.440909 Sum=2.838849 Log. 23=1.36 1728 ^ns. 130.00=1.477121 EXPLANATION OF THE TABLE OF LOGARITHMIC SINES AND TANGENTS. This table consists merely of logarithms, calculated for the numbers which express the lengths of the natural sines and tangents, to every minute of a quadrant, whose radius is 10,000,000,000. The logarithm of RADIUS, of the sine of 90°, and of the tangent of 45°, will, of course, be lO.OOOOOO. As there is frequent necessity to employ the numbers in this table, the following rules must be thoroughly understood. To FIND THE LOGARITHMIC SINE, CO-SINE, TANGENT, OR CO-TANGENT OF ANY NUMBER OF DEGREES, OR DEGREES AND MINUTES. If the degrees are less than 45, look for them at the top of thepage^ and for the minutes^ in the left hand column ; under the given name^ and op- posite the minutes, will be found the logarithm sought. But, if the degrees are between 45 and 90, look for them at the bottom of the page^ and for the minutes^ in the right hand column : over the given name, and opposite the minutes, will be found the logarithm sought. If the angle be more than 90°, find the log. for its supplement, and it will be \L2 log. required. 8 TRAVERSE TABLE. The secants and co-secants are not often employed in trigonometrical calculations, and are therefore omitted in the annexed table. They may easily be found, if desired, by the following rule. The logarithmic SECA^-T of an angle is found by suethactixg the LOGARITHMIC CO-SINE OF THE SAME ANGLE FROM 20.000000 : and The LOGARITHMIC CO-SECANT IS FOUND BY SUBTRACTING THE LOGARITH- MIC SINE FROM 20.000000. Thus, find the secant of 31° 20'. 20.000000 Co-sin. 31° 20'= 9.931537 Rem. = sec. 31° 20=10.068463 Find the co-sec. of 47° 38'. 20.000000 Sin. 47° 38= 9.868555 Rem. = co-sec. 47° 38'=10.131445 When there are seconds^ the column headed D is employed. The numbers in this column show how much difference must be allowed in the log. for every second. This difference is carried to two places of decimals. Hence the reason of the following rule. To find a sine or tangent to degrees^ minutes^ and seconds. Find for degrees and minutes as before ; then multiply the opposite number in the column D, by the seconds, cut off two figures from the right of the product, and add what is left to the log. before found. For co-sines and co-tangents^ this product must be subtracted^ instead of being added. To FIND THE DEGREES, OR DEGREES AND MINUTES, ANSWERING TO ANY GIVEN LOGARITHMIC SINE, CO-SINE, TANGENT, OR CO-TANGENT. • Under or over the proper name in the table, seek the given log. or the one nearest to it : the degrees will be found at the same extremity of the page as the name, and the minutes at the left or right, according as the name is at the top or bottom. To find an angle to seconds, subtract from the given log, the next less in the table, annex two ciphers to the remainder, and divide it, thus augmented, by the tabular difference. The quotient is seconds, to be added to the degrees and minutes of the tabular log. in case of sines and tangents, but to be subtracted, in case of co-sines and co-tangents. Explanation of the traverse table, or table of dif- ference of latitude and departure, This is calculated for degrees and quarters of degrees, and for any distance up to 100 rods, chains, &c. ; by which the northings and south- ings, eastings and westings made in a survey may be found. Note. Northings and southings are called difference of latitude, or simply latitude ; eastings and westings are called departure, meridi- an distance, or longitude. To find the latitude and departure^ or northings kc.for any course and distance. If the course be less than 45°, look for it at the top, but if more than NATURAL SINES. 9 45° at the bottom of the page, and look for the distance in the right or left hand column ; against the distance, and directly under or over the course, stand the northing, &;c. in whole numbers and decimals. If the course be less than 45°, the northing or southing will be greater than the easting or westing ; but if more than 45°, the easting or west- ing will be the greatest. When the distance exceeds 100, take any two or more numbers, which, added together, will equal the distance, and find the latitude and departure for each of these numbers; add the several latitudes to- gether, and the sum will be the whole latitude ; and so for the depar- ture. And when the distance is in chains and links, or whole numbers tind decimals, find the latitude, &:c. for the chains or whole numbers, and then for the links or decimals, remembering to remove the decimal point in the table further to the left, according to the given decimal. 1. Required the latitude and departure for 45 rods^ on a course N. 15° 15' W. Under 15° 15' and against 45 is 43.42 for the northing, and 11.84 for the westing. 2. Required the latitude and departure for 120 rods^ on a course S. 58° 30' E. Take one third of 120, which is 40 ; against this number, over 58° 30', is 20.90 for the latitude, and 34.11 fox the departure. These mul- tiplied by 3 give 62.70 for the southing, and 102.33 for the easting. 3. Required the latitude and departure for 37.36 rods^ or 37 chains and 36 links^ on a course N. 26° 45' E. For 37. Lat. 33.04 Dep. 16.65 0.36 .32 .16 37.36 33.36 16.81 Northing 33.36 Easting 16.81 Note. — When the minutes are not 15, 30, or 45, the northings, &c. must be calculated by natural sines, or by trigonometry. When the latitude and departure are themselves given, the course and distance may be found in the table, thus : look along the columns of latitude and departure, until the given numbers are found opposite each other. Tlie course will then be directly under or over them, and the distance in the right or left hand column. If the numbers cannot be exactly found, take those which come near- est. If either or both are too great to be found in the table, divide both by any number, (10, 100, 1,000, &c. is most convenient,) and use the quotients. The course found thus will be the one required, but the distance must be multiplied by the number used before as a divisor. Explanation of the table of natural sines. Natural Sines are decimals bearing the same proportion to unity or 1, that the sine of the corresponding number of degrees and minutes bears to radius, or sine of 90°. That is, 1 is assumed as the nat. sine of 90°, and the table calculated accordingly, M 10 NATURAL SINES. TO FIND THE NATURAL SIXE OF AM NUMBER OF DEGREES AND MINL'TES. If the degrees be less than 45, look for them at the top of the col- umns, and for the minutes at the left hand ; but if more than 45, look for them at the bottom, and for the minutes at the right hand ; under or over the degrees and against the minutes, will be the natural sine re- quired. The reverse of this will give the degrees and minutes corresponding to any natural sine. TO CALCULATE THE NORTHING OR SOUTHING, ScC FOR ANT COURSE AND DI5TANCK, BY NATURAL SINES. Find the nat. sine and co-sine of the course, and into each of these multiply the distance ; the products will be the latitude and departure required. Required the latitude and departure for 6 chains and 22 links on a course N. 38^ 27' W. Nat. sine of 38^ 27', 0.62183 Nat. co-sine 0.78315 6.22 6.22 124366 156630 124366 156630 373098 469890 3.8677826 4.8711930 Answer. Northing 4.87 Westing 3.87 A TABLE OF LOGARITHMS OF NUMBERS FROM 1 TO 10,000. N. L.,;'i. N. Lojr. N. Lug. s. Loo. 1 0.000000 26 1.414973 51 1 . 707570 76 1.880814 2 0.301030 27 1.431364 52 1.716003 77 1.886491 3 0.477121 28 1.447158 53 1.724276 78 1.892095 4- 0.602060 29 1.462398 54 1 . 732394 79 1.897627 5 0.698970 30 1.477121 55 1 . 740363 80 1.903090 6 0.778151 31 1.491362 56 1.748188 81 1.908485 7 0.845098 32 1.505150 57 1.755875 82 1.913814 8 0.903090 33 1.518514 58 1.763428 83 1.919078 9 0.954243 34 1.531479 59 1.770852 84 1.924279 10 1.000000 35 1.544068 60 1.778151 85 1.929419 li 1.041393 36 1.556303 61 1.785330 86 1.934498 12 1.079181 37 1.568202 62 1.792392 87 1.939519 13 1.113943 38 1.579784 63 1 . 799341 88 1.944483 14 1.146128 39 1.591065 64 1.806180 89 1.949390 15 1.176091 40 1.602060 65 1.812913 90 1.954243 16 1.204120 41 1.612784 66 1.819544 91 1.959041 17 1.230449 42 1.623249 67 1.826075 92 1.963788 18 1.255273 .43 1.633468 68 1.832509 93 1.968483 19 1.278754 44 1.643453 69 1.838849 94 1.973128 5iO 1.301030 45 1.653213 70 1.845098 95 1.977724 21 1.322219 46 1.662758 71 1.851258 96 1.982271 22 1.342423 47 1.672098 72 1.857333 97 1.986772 23 1.361728 48 1.681241 73 1.863323 98 1.991226 24 1.380211 49 1.690196 74 1.869232 99 1.995635 25 1.397940 50 1.698970 75 1.875061 100 2.000000 N.B. In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O'Sj points or dots are introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. A TABLE OF LOGARITHMS FP.OM i TO 10,000. [ N. 1 1 1 1 2 i 3 i 4 i 5 i 6 1 7 1 8 1 9 1 D 1 100 000000 04341 0868 1301 1734 2i66| 2698| 3U29| 3461 3891 432 101 4321 4751 5181 5609 6038 6466 6894 73211 7748 8174 428 102 8000 9026 9451 9876 .300 .724 1147 1570 1993 2415 424 103 012837 3259 3680 4100 4521 4940 5360 5779 6197 6616 419 104 7033 7451 7868 8284 8700 9116 9532 9947 .361 .775 416 105 021189 1603 2016 2428 2841 3252 3664 4075 4486 4896 412 106 5306 5715 6125 6533 6942 7350 7757 8164 8571 8978 408 107 9384 9789 .195 .600 1004 1408 1812 2216 2619 3021 404 108 033424 3826 4227 4628 5029 5430 5830 6230 6629 7028 400 109 110 7426 7825 8223 8620 2576 9017 9414 3362 9811 3755 .207 .602 .998 4932 396 393 041393 1787 2182 2969 4148 4540 111 5323 5714 6105 6495 6885 7275 7664 8053 8442 8830 389 112 9218 9606 9993 .380 .766 1153 1538 1924 2309 2694 386 113 053078 3463 3846 4230 4613 4996 5378 5760 6142 6524 382 114 6905 7286 7666 8046 8426 8805 9185 9563 9942 .320 379 115 060698 1075 1452 1829 2206 2582 2958 3333 3709 4083 376 116 4458 4832 5206 5580 5953 6326 6699 7071 7443 7815 372 117 8186 8557 8928 9298 9668 ..38 .407 .776 1145 1514 369 118 071882 2250 2617 2985 3352 3718 4085 4451 4816 5182 366 119 120 5547 5912 6276 6640 .266 7004 .626 7368 7731 1347 8094 1707 8457 8819 363 360 079181 9543 9904 .987 2067 2426 121 082785 3144 3503 3861 4219 4576 4934 5291 5647 6004 357 122 6360 6716 7071 7426 7781 8136 8490 8845 9198 9552 355 123 9905 .258 .611 .963 1315 1667 2018 2370 2721 3071 351 124 093422 3772 4122 4471 4820 5169 5518 5866 6215 6562 349 125 6910 7257 7604 7951 8298 8644 8990 9335 9681 ..26 346 126 100371 0715 1059 1403 1747 2091 2434 2777 3119 3462 343 127 3804 4146 4487 4828 5169 5510 5851 6191 6531 6871 340 128 7210 7549 7888 8227 8565 8903 9241 9579 9916 .253 338 129 130 110590 0926 4277 1283 4611 1599 4944 1934 5278 2270 2605 5943 2940 3275 3609 6940 335 333 113943 5611 6276 6608 131 7271 7603 7934 8265 8595 8926 9256 9586 9915 .245 330 132 120574 0903 1231 1560 1888 2216 2544 2871 3198 3525 328 133 3852 4178 4504 4830 5156 5481 5806 6131 6456 6781 325 134 7105 7429 7753 8076 8399 8722 9045 9368 9690 ..12 323 135 130334 0655 0977 1298 1619 1939 2260 2580 2900 3219 321 136 3539 3858 4177 4496 4814 5133 5451 5769 6086 6403 318 137 6721 7037 7354 7671 7987 8303 8818 8934 9249 9564 315 138 9879 .194 .508 .822 1136 1450 1763 2076 2389 2702 314 139 140 143015 3327 6438 3639 6748 3951 7058 4263 4574 7676 4885 5196 8294 5507 8603 5818 311 309 146128 7367 7985 8911 141 9219 9527 9835 .142 .449 .756 1063 1370 1676 1982 307 142 152288 2594 2900 3205 3510 3815 4120 4424 4728 5032 305 143 5336 5640 5943 6246 6549 6852 7154 7457 7759 8061 303 144 8362 8664 8965 9266 9587 9868 .168 .469 .769 1068 301 145 161368 1667 1967 2266 2564 2863 3161 .3460 3758 4055 299 146 4353 4650 4947 5244 5541 5838 6134 6430 6726 7022 297 147 7317 7613 7908 8203 8497 8792 9086 9380 9674 9968 295 148 170262 0555 0848 1141 1434 1726 2019 2311 2603 2895 293 149 150 3186 3478 3769 4060 4351 4641 4932 5222 5512 5802 8689 291 289 176091 6381 6670 6959 7248 7536 7825 8113 8401 151 8977 9264 9552 9839 .126 .413 .699 .985 1272 1558 287 152 181844 2129 2415 2700 2985 3270 3555 3839 4123 4407 285 153 4691 4975 5259 5542 5825 6108 6391 6674 6956 7239 283 154 7521 7803 8084 8366 8647 8928 9209 9490 9771 ..51 281 155 190332 0612 0892 1171 1451 1730 2010 2289 2567 2846 279 156 3125 3403 3681 3959 4237 4514 4792 5069 5346 5623 278 157 5899 6176 6453 6729 7005 7281 7556 7832 8107 8382 276 158 8657 8932 9206 9481 9755 ..29 .303 .577 .850 112412741 159 i 201397 1670 1943 2216 2488 27611 3033 3305 3577 38481272 N. i ! 1 1 2 i 3 1 4 ! 5 1 6 1 7 1 8 ! 9 1 D. 1 A TABLE OP LOGARITHMS PHOM 1 TO 10,000 3 N. 1 ll|2|3|4|5|6l7|8!9|D. 1 160 204120 4391 466314934 5204 5475 5746 6016 6286 6.556 271 161 6826 7096 7365 7634 7904 8173 8441 8710 8979 9247 269 163 9515 9783 ..5l! .319 .586 .853 1121 1388 1654 1921 267 163 212188 2454 2720J 2986 3252 3518 3783 4049 4314 4579 266 164 4844 5109 5373; 5638 5902 6166 6430 6694 6957 7221 264 165 7484 7747 80l0i 8273 8536 8798 9060 9323 9.585 9846 262 166 220108 0370 063110892 1153 1414 1675 1936 2196 2456 261 167 2716 2976 3236 i 3496 3755 4015 4274 4533 4792 5051 259 168 5309 5568 5826! 6084 6342 6600 6858 7115 7372 7630 258 169 170 7887 8144 0704 8490 8657 8913 9170 1724 9426 9682 2234 9938 .193 256 254 230449 0960 1215 1470 1979 2488 2742 171 2996 3250 3504 3757 4011 4264 4517 4770 5023 5276 253 172 5528 5781 6033 6285 6537 6789 7041 7292 7544 7795 252 173 8046 8297 8548 8799 9049 9299 9550 9800 ..50 .300 250 174 240549 0799 1048 1297 1546 1795 2044 2293 2541 2790 249 175 3038 3286 3534 3782 4030 4277 4525 4772 .5019 .5266 248 176 5513 5759 6006 6252 6499 6745 6991 7237 7482 7728 246 177 7973 8219 8464 8709 8954 9198 9443 9687 9932 .176 245 178 250420 0664 0908 1151 1.395 1638 1881 2125 2368 2610 243 179 180 2853 3096 5514 3338 5755 3580 3822 6237 4064 6477 4306 6718 4548 6958 4790 5031 7439 242 241 255273 5996 7198 181 7679 7918 8158 8398 8637 8877 9116 9355 9594 9833 239 182 260071 0310 0548 0787 1025 1263 1501 1739 1976 2214 233 183 2451 2688 2925 3162 3399 3638 3873 4109 4346 4582 237 184 4818 5054 5290 5525 5761 5996 6232 6467 6702 6937 235 185 7172 7406 7641 7875 8110 834-4 8578 8812 9046 9279 234 186 9513 9746 9989 .213 .446 .679 .912 1144 1377 1609 233 187 271842 2074 2306 2538 2770 3001 3233 3464 3696 3927 232 188 4158 4389 4G20 4850 5081 5311 5542 5772 6002 6232 230 189 190 6462 6692 8982 6921 9211 7151 7380 9667 7609 9895 7838 .123 8087 .351 8296 .578 8525 .806 229 228 278754 9439 191 281033 1261 1488 1715 1942 2169 2396 2822 2849 3075 227 192 3301 3527 3753 3979 4205 4431 4656 4882 5107 5332 226 193 5557 5782 6007 6232 6456 6681 6905 7130 7354 7578 225 194 7802 8026 8249 8473 8696 8920 9143 9386 9589 9812 223 195 290035 0357 0480 0702 0925 1147 1369 1591 1813 2034 222 198 2256 2478 2699 2920 3141 3363 3584 3804 4025 4246 221 197 4466 4687 4907 5127 5347 5567 5787 6007 6226 6446 220 198 6665 6884 7104 7323 7542 7761 7979 8198 8416 8635 219 199 200 8853 9071 1247 9289 1464 9507 1681 9725 1898 9943 .161 .378 .595 2764 .813 2980 218 217 301030 2114 2331 2547 201 3196 3412 3828 3844 4059 4275 4491 4706 4921 5136 216 202 5351 5566 5781 .5996 6211 6425 6639 6854 7068 7282 215 203 7496 7710 7924 8137 8351 8564 8778 8991 9204 9417 213 204 9630 9843 ..56 .268 .481 .693 .906 1118 1330 1542 212 205 311754 1966 2177 2389 2600 2812 3023 3234 3445 3656 211 200 3867 4078 4289 4499 4710 4920 5130 5340 5551 5760 210 207 5970 6180 6390 6599 6809 7018 7227 7436 7646 7854 209 208 8063 8272 8481 8689 8898 9106 9314 9522 9730 9938 208 209 210 320146 0354 2426 0562 2633 0769 2839 0977 3046 1184 1391 3458 1598 3665 1805 3871 2012 207 206 322219 3252 4077 211 4282 4488 4694 4899 5105 5310 5516 5721 5926 6131 205 212 6336 6541 6745 6950 7155 7359 7563 7767 7972 8176 204 213 8380 8583 8787 8991 9194 9398 9601 9805 ...8 .211 203 214 330414 0617 0819 1022 1225 1427 1630 1832 2034 2236 202 215 2438 2640 2842 .3044 3246 3447 36491 3850 4051 4253 202 216 4454 4055 4856 5057 5257| 5458 5658 5859 6059 6360 201 217 6460! 6860 6860 7060 7260 7459 7659 7858 8058 8257 200 218 84561 8656 8855 9054 9253 9451 9650 9849 ..47 .246 199 219 340444 0642' 0841 1039 1237 14.35' 1632 1830' 2028 2225' 198 N. 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 i 8 i 9 i D. « 4 A TABLE OP LOGARITHMS FROM 1 TO 10,000. N. ^i ilf2|3|4|5l6|7l8|9|D. 1 220 342423, 2620 2817 3014 3212, 3409 3606 3802 3999 4196 197 221 4392' 4589 4785 4981 5178 6374 5570 5768 5962 6157 196 2^2 6353 6549 6744 6939 7135 7330 7525 7720 7915 8110 195 223 8305 8500 8694 8889 9083 9278 9472 9666 9860 ..54 194 224 350248 0442 0636 0829 1023 1216 1410 1603 1796 1989 193 225 2183 2375 2568 2761 2954 3147 3339 3532 3724 3916 193 226 4108 4301 4493 4885 4876 5068 5260 6452 5643 5834 192 227 6026 6217 6408 6599 6790 6981 7172 7363 7554 7744 191 ■228 7935 8125 8316 8506 8696 8886 9076 9266 9456 9646 190 239 230 9835 ..25 .215 2105 .404 2294 .593 2482 .783 2671 .972 2859 1161 3048 1350 3236 1539 3424 189 188 361728 1917 231 3612 3800 3988 4176 4363 4561 4739 4926 5113 5301 188 232 5488 5675 5862 6049 6236 6423 6610 6796 6983 7169 187 233 7356 7542 7729 7915 8101 8287 8473 8659 8846 9030 186 234 9216 9401 9587 9772 9958 .143 .328 .513 .698 .883 185 235 371068 1253 1437 1622 1808 1991 2176 2360 2644 2728 184 236 2912 309o 3280 3464 3647 3831 4015 4198 4382 4565 184 237 4748 4932 5115 5298 5481 5664 6846 6029 6212 6394 183 238 6577 6759 6942 7124 7306 7488 7670 7862 8034 8216 182 239 240 8398 8580 0392 8761 8943 9124 0934 9306 1115 9487 1296 9688 1476 9849 1656 ..30 1837 181 181 380211 0573 0754 241 2017 2197 2377 2557 2737 2917 3097 3277 3456 3636 180 242 3815 3995 4174 4353 4533 4712 4891 5070 6249 5428 179 243 5606 5785 5964 6142 6321 6499 6877 6856 7034 7212 178 244 7390 7568 7746 7923 8101 8279 8456 8634 8311 8989 178 245 9166 9343 9520 9698 9875 ..51 .228 .405 .582 .759 177 246 390935 1112 1288 1464 1641 1817 1993 2169 2345 2521 176 247 2697 2873 3048 3224 3400 3575 3751 3926 4101 4277 176 248 4452 4627 4302 4977 5152 5326 6501 5676 6850 6025 175 249 6199 6374 6548 6722 6896 7071 7245 7419 7692 7766 174 250 397940 8114 8287 8461 8634 8808 8981 9154 9328 9601 173 251 9674 9847 ..20 .192 .365 .538 .711 .883 1056 1228 173 252 401401 1573 1745 1917 2089 226 i 2433 2605 2777 2949 172 253 3121 3292 3464 3635 3807 3978 4149 4320 4492 4663 171 254 4834 5005 5176 5346 5517 5688 5858 6029 6199 6370 171 255 6540 6710 6881 7051 7221 7391 7561 7731 7901 8070 170 256 8240 8410 8579 8749 8918 9087 9257 9426 9596 9764 169 257 9933 .102 .271 .440 .609 .777 .948 1114 1283 1451 169 258 411620 1788 1956 2124 2293 2461 2829 2796 2964 3132 168 259 260 3300 3467 5140 3635 5307 3803 5474 3970 5641 4137 5808 4305 5974 4472 6141 4639 6308 4806 6474 167 167 414973 261 6641 6807 6973 7139 7306 7472 7638 7804 7970 8135 166 262 8301 8467 8633 8798 8964 9129 9295 9^i60 9625 9791 165 263 9956 .121 .286 .451 .616 .78! .946 1110 1275 1439 165 264 421604 1768 1933 2097 2261 2426 2590 2754 2918 3032 164 265 3246 3410 3574 3737 3901 4085 4228 4392 4565 4718 164 266 4882 5045 5208 5371 5534 5697 5860 6023 6186 6349 163 267 6511 6674 6836 6999 7161 7324 7486 7648 7811 7973 162 268 8135 8297 8459 8621 8783 8944 9106 9268 9429 9591 162 269 270 9752 9914 1525 ..75 1685 .236 1846 .398 2007 .559 2167 .720 2328 .881 2488 1042 2649 1203 2809 161 161 431364 271 2969 3130 3290 3450 3610 3770 3930 4090 4249 4409 160 272 4569 4729 4888 5048 5207 .5367 5526 5685 6844 6004 159 273 6163 6322 6481 6640 6798 6957 7116 7275 7433 7592 169 274 7751 7909 8067 8226 8384 8542 8701 8869 9017 9175 158 275 9333 9491 9648 9806 9964 .122 .279 .437 .594 .752 158 276 440909 1066 1224 1381 1538 1695 1852 2009 2166 2323 157 277 2480 2637 2793 2950 3106 3263 3419 3676 3732 3889 157 278 4045 4201 4357 4513 4669 4826 4981 5137 5293 5449 166 279 6604 5760 5915 607116226 6382 6637 6692 6848 7003 155 N. i 1 1 1 2 1 3 I 4 1 5 1 6 i 7 1 .8 1 9 1 D-l A TABLE OF LOGARITims 1 EOM 1 TO 10,000. b N. |l|2|3|4l5|6|7i8l9|D. I 280 447158 73131 7468 7623 7778 7933 8088 8242 8397| 8552 155 281 8706 8861 9015 9170 9324 9478 9633 9787 9941 ..95 154 282 450249 0403 0557 0711 0865 1018 1172 1326 1479 1633 154 283 1786 1940 2093 2247 2400 2553 2706 2859 3012 3165 153 284 3318 3471 3624 3777 3930 4082 4235 4387 4540 4692 153 285 4845 4997 5150 5302 5454 5606 5758 5910 6062 6214 1.52 286 6366 6518 6670 6821 6973 7125 7276 7428 7579 7731 152 287 7882 8033 8184 8336 8487 8638 8789 8940 9091 9242 151 288 9392 9543 9694 9845 9995 .146 .296 .447 .597 .748 151 289 290 460898 1048 2548 1198 2697 1348 2847 1499 2997 1649 1799 3296 1948 3445 2098 3594 2248 3744 150 150" 462398 3146 291 3893 4042 4191 4340 4490 4639 4788 4936 5085 5234 149 292 6383 5532 5680 5829 5977 6126 6274 6423 6571 6719 149 293 6868 7016 7164 7312 7460 7608 7756 7904 8052 8200 148 294 8347 8495 8643 8790 8938 9085 9233 9380 9527 9675 148 295 9822 9969 .116 .263 .410 .557 .704 .851 .998 1145 147 296 471293 1438 1585 1732 1878 2025 2171 2318 2464 2610 146 297 2756. 29031 3049 3195 3341 3487 3633 3779 3925 4071 146 298 4216 43621 4508 4653 4799 4944 5090 5235 5381 5526 146 299 300 5671 477121 5816 5962 7411 6107 7555 6252 7700 6397 6542 6687 8133 6832 8278 6976 8422 145 145 7266 7844 7989 301 8566 8711 8855 8999 9143 9287 9431 9575 9719 9863 144 302 480007 0151 0294 0438 0582 0725 0869 1012 1156 1299 144 303 1443 1586 1729 1872 2016 2159 2302 2445 2588 2731 143 304 2874 3016 3159 3302 3445 3587 3730 3872 4015 4157 143 305 4300 4442 4585 4727 4869 5011 5153 5295 5437 5579 142 306 5721 5863 6005 6147 6289 6430 6572 6714 6855 6997 142 307 7138 7280 7421 7563 7704 7845 7986 8127 8269 8410 141 308 8551 8692 8833 8974 9114 .520 9255 9396 9537 9677 9818 141 309 310 9958 ..99 .239 .380 .661 .801 2201 .941 2341 1081 1222 2621 140 140 491362 1502 1642 1782 1922 2062 2481 311 2760 2900 3040 3179 3319 3458 3597 3737 3876 4015 139 312 4155 4294 4433 4572 4711 4850 4989 5128 5267 5406 139 313 5544 5683 5822 5960 6099 6238 6376 6515 6653 6791 139 314 6930 7068 7206 7344 7483 7621 7759 7897 8G35 8173 138 315 8311 8448 8586 8724 8862 8999 9137 9275 9412 9550 138 316 9687 9824 9962 ..99 .236 .374 .511 .648 .785 .922 137 317 501059 1196 1333 1470 1607 1744 1880 2017 2154 2291 137 318 2427 2564 2700 2837 2973 3109 3246 3382 3518 3655 136 319 320 3791 3927 5286 4063 5421 4199 6557 4335 5693 4471 5828 4607 4743 4878 6234 5014 6370 136 136 505150 6964 6099 321 6505 6640 6776 6911 7046 7181 7316 7461 7586 7721 135 332 7856 7991 8126 8260 8395 8530 8664 8799 8934 9068 135 323 9203 9337 9471 9606 9740 9874 ...9 .143 .277 .411 134 324 510545 0679 0813 0947 1081 1215 1349 1482 1616 1750 134 325 1883 2017 2151 2284 2418 2551 2684 2818 2951 3084 133 326 3218 3351 3484 3617 3750 3883 4016 4149 4282 4414 133 327 4548 4681 4813 4946 5079 5211 5344 5476 5609 5741 133 328 5874 6006 6139 6271 6403 6535 6668 6800 6932 7064 132 329 330 7196 7328 8646 7460 8777 7592 8909 7724 7855 9171 7987 9303 8119 8251 8382 9697 132 131 518514 8040 9434 9566 331 9828 9959 ..90 .221 .353 .484 .615 .745 .876 1007 131 332 521138 1269 1400 1530 1661 1792 1922 2053 2183 2314 131 333 2444 2575 2705 2835 2966 3096 3226 3356 3486 3616 130 334 3746 3876 4006 4136 4266 4396 4526 4656 4785 4915 130 335 5045 5174 5304 5434 5563 5693 5822 5951 6081 6210 129 336 6339 6469 6598 6727 6856 6985 7114 7243 7372 7501 129 337 7630 7759 7888 8016 8145 8274 8402 8531 8660 8788 129 338 8917 9045 9174 9302 9430 9559 9687 9815 9943 ..72 128 339 530200 0328 0456 05841 0712 0840 0968 1096 1223 1351 128 , N. 1 |l!2|3|4|5|6|7|8|9|D. 1 A TABLE OP L0GAKITU?,i3 FI1031 1 TO 10,000. r i |l|2|3i4|6|6|7|8|9!D. 1 1340 531479 1607 1734 i 1862 1990 2117 2245 2372! 2500 2627 128 341 2754 2882 3009 3136 3264 3391 3518 3645 13772 3899 127 342 4026 4153 4280 4407 4534 4661 4787 4914 1 5041 5167 127 343 5294 5421 5547 5674 5800 5927 6053 6180 6306 6432 126 344 6558 6085 6811 6937 7063 7189 7315 7441 7567 7693 126 345 7819 7945 8071 8197 8322 8448 8574 8699 8825 8951 126 346 9076 9202 9327 9452 9578 9703 9829 9954 ..79 .204 125 347 540329 0455 0580 0705 0830 0955 1080 1205 1330 1454 125 348 1579 1704 1S29 1953 2078 2203 1 2327 2452 ! 2576 2701 125 349 350 2825 2950 4192 3074 3199 44-40 3323 3447 3571 4812 3696 4936 3830 5060 3944 5183 124 124 544088 4316 4564 4688 351 5307 5431 5555 5678 5802 5925 6049 6172 6296 6419 124 352 6543 6666 6789 6913 7036 7159 7282 7405 ■ 7529 7652 123 353 7775 7898 80311 S144 8267 8389 8512 8635 8758 8881 123 354 9003 9126 9249i 9371 9494 9616 9739 9861 9984 .106 123 355 550228 0351 0473 0595 07'7 0840 0902 1084 1206 1.328 122 356 1450 1572 1694 1816 1938 2060 2181 2303 2425 2547 122 357 2668 2790 2911 3033 3155 3276 3398 3519 3640 3762 121 358 3883 4004 4126 4247 4368 4489 4610 4731 4852 4973 121 359 360 5094 5215 5336 5457 5578 6785 5699 6905 5820 7026 5940 7146 6061 7267 6182 7387 121 120 556303 6423 6544i 6664 361 7507 7627 7748 j 7868 7988 8108 8228 8349 8469 8589 120 362 8709 8829 8948 9068 9188 9308 9428 9548 9667 9787 120 363 9907 ..26 .146 .265 .385 .504 .624 .743 .863 .982 119 364 561101 1221 1340 1459 1578 1698 1817 1936 2055 2174 119 365 2293 2412 2531 2650 2769 2887 3006 3125 3244 3362 119 366 3481 3600 3718 3837 3955 4074 4192 4311 4429 4548 119 367 4666 4784 4903 5021 5139 6257 5376 5494 5612 5730 118 363 5848 5986 6084 6202 6320 6437 0555 6673 6791 6909 118 389 370 7026 568202 7144 7262 8436 7379 8554 7497 8671 7614 8788 7732 8905 7849 9023 7967 9140 8084 9257 118 117 8319 371 9374 9491 9608 9725 9842 9959 ..76 .19o .309 .426 117 372 570543 0660 0776 0893 1010 1126 1243 1359 1476 1.592 117 373 1709 1825 1942 2058 2174 2291 2407 2523 2639 2765 116 374 2872 2988 3104 3220 3336 3452 3568 3684 3800 3915 116 375 4031 4147 4263 4379 4494 4610 4726 4841 4957 5072 116 376 5188 5303 5419 5534 5650 5765 5880 5996 6111 6226 115 377 6341 6457 6572 6687 6802 6917 7032 7147 7262 7377 115 378 7492 7607 7722 7836 7951 8066 8181 8295 8410 8525 115 379 380 8639 8754 8868 ..12 8983 .126 9097 9212 .355 9326 .469 9441 .583 9555 9669 114 114 579784 989S .241 .697 .811 381 580925 1039 1153 1267 1381 1495 1608 1722 1336 1950 114 382 2063 2177 2291 2404 2518 2631 2745 2868 2972 3035 114 383 3199 3312 3426 3539 3852 3765 .3879 3992 4105 4218 113 334 4331 4444 4557 4670 4783 4896 5009 6122 5235 6348 113 385 5461 5574 5686 5799 5912 6024 6137 6250 6362 6475 113 386 6587 6700 6812 6925 7037 7149 7262 7374 7486 7599 112 387 7711 7823 7935 8047 8160 8272 8384 8496 8608 8720 112 388 8832 8944 9056 9167 9279 9391 9503 9815 9726 9838 112 389 390 9950 ..61 1176 .173 1287 .284 1399 .396 1510 .507 1021 .619 .739 .842 1955 .953 112 111 591065 1733 1843 2066 391 2177 2288 2399 2510 2621 2732 2843 2S54 3064 3175 111 392 3286 3397 3508 3618 3729 3840 3950 4061 4171 4282 111 393 4393 4503 4614 4724 4834 4945 5055 5165 5276 5386 110 394 5496 5606 5717 5827 5937 6047 6157 6267 6377 6487 110 395 6597 6707 6817 6927 7037 7146 7256 7366 7476 7586 110 396 7695 7805 7914 8024 8134 8243 8353 8462 8572 8681 110 397 8791 8900 9009 9119 9228 9337 9446 9556 9665 9774 109 398 9883 9992 .101 .210 .319 .428 .537 .646 .755 .864 109 399 600973 1082 1191 1299 1408 1517 1625 1734 1843 1951 109 N. 1 1 1 2 1 3 1 4 1 5 i 6 1 7 1 8 1 9 1 D. 1 A TABLE OF L0GAIllTiI3lS FROM 1 TO 10,000. H 1 1 1 2 1 3 1 4 1 5 i 6 1 7 ! 8 1 9 1 D j 400 602060 2169 2277 23S0 2494 2603 2711 2819 2928) 3036' 108 f 401 3144 3253 3361 3469 3577 3686 3794 3902 4010 4118 108 402 4226 4334 4442 4550 4658 4766 4874 4982 5089 5197 108 403 5305 5413 5521 5628 5736 5844 5951 6059 6166 6274 108 404 6381 6489 6596 6704 6811 6919 7026 7133 7241 7348 107 405 7455 7562 7669 7777 7884 7991 8098 8205 8312 8419 107 406 8526 8633 8740 8847 8954 9061 9167 9274 9381 9488 107 407 9594 9701 9808 9914 ..21 .128 .234 .341 .447 .554 107 408 610660 0767 0873 0979 1086 1192 1298 1405 1511 1617 106 409 410 1723 1829 1936 2042 2148 2254 2360 2466 3525 2572 2678 3736 106 106 612784 2890 2996 3102 3207 3313 3419 3630 411 3842 3947 4053 4159 4284 4370 4475 4581 4686 4792 106 412 4897 5003 5108 5213 5319 5424 5529 5634 5740 5845 105 413 5950 6055 6160 6265 6370 6476 6581 6686 6790 6895 105 414 7000 7105 7210 7315 7420 7525 7629 7734 7839 7943 105 415 8048 8153 8257 8362 8466 8571 8676 8780 8884 8989 105 416 9093 9198 9302 9406 9511 9615 9719 9824 9928 ..32 104 417 620136 0240 0344 0448 0552 0656 0760 0864 0968 1072 104 418 1176 1280 1384 1488 1592 1695 1799 1903 2007 2110 104 419 420 2214 2318 3353 2421 3456 2525 3559 2628 2732 2835 2939 3042 3146 104 103 623249 3663 3766 3869 3973 4076 4179 421 4282 4385 4488 4591 4695 4798 4901 5004 5107 5210 103 422 6312 5415 5518 5621 5724 5827 5929 6032 6135 6238 103 423 6340 6443 6546 6648 6751 6853 6956 7058 7161 7263 103 424 7366 7468 7571 7673 7775 7878 7980 8082 8185 8287 102 425 8389 8491 8593 8695 8797 8900 90021 9104 9206 9308 102 426 9410 9512 9613 9715 9817 9919 ..211 .123': .324 .326i 102 1 427 630428 0530 0631 0733 0835 0936 1038 11391 1241 1342 102 428 1444 1545 1647 1748 1849 1951 2052 2153 2255 2356 101 429 430 2457 2559 3569 2660 3670 2761 2862 2963 3064 3165 4175 3266 4276 3367 4376 101 100 633468 3771 3872 3973 4074 431 4477 4578 4679 4779 4880 4981 5081 5182 5283 5383 100 432 5484 55S4 5685 5785 5886 5986 6087 6187 6287 6388 100 433 6488 6588 6688 6789 6889 6989 7089 7189 7290 7390 100 434 7490 7590 7690 7790 7890 7990 8090 8190 8290 8389 99 435 8489 8589 8889 8789 8888 8988 9088 9188 9287 9387 99 436 9486 9588 9686 9785 9885 9984 ..84 .183 .283 .382 99 437 640481 0581 0680 0779 0879 0978 1077 1177 1276 1375 99 438 1474 1573 1672 1771 1871 1970 2069 2168 2267 2366 99 439 440 2465 2563 2662 3650 2761 3749 2860 3847 2959 3058 3156 3255 4242 3354 4340 99 98 643453 3551 3946 4044 4143 441 4439 4537 4636 4734 4832 4931 5029 5127 5226 5324 98 442 5422 5521 5619 5717 5815 5913 6011 6110 6208 6306 98 443 6404 6502 6600 6698 6796 6894 6992 7089 7187 7285 98 444 7383 7481 7579 7670 7774 7872 7969 8067 8165 8262 98 445 8360 8458 8555 8653 8750 8848 8945 9043 9140 9237 97 446 9335 9432 9530 9627 9724 9821 9919 ..16 .113 .210 97 447 650308 0405 0502 0599 0696 0793 0890 0987 1084 1181 97 44S 1278 1375 1472 1569 1666 1762 1859 1956 i 2053 2150 97 449 450 2246 2343 3309 2440 3405 2536 3502 2633 359S 2730 3695 2326 2923 3019 3116 4080 97 96 653213 3791 3888 3984 451 4177 4273 4369 4455 4562 4658 4754 4850 4946 50421 961 452 5138 5235 5331 5427 5523 5619 5715 5810 5906 6002 96 453 6098 6194 6290 6386 6482 6577 6673 6769 6864 6960 96 454 7056 7152 7247 7343 7438 7534 7629 77251 7820 7916 96 455 8011 8107 8202 8298 8393 8488 8584 8679 8774 8870 95 456 8965 9060 9155 9250 9346 9441 9536 9631 9726 9821 95 457 9916 ..11 .106 .201 .296 ..391 .486 .581 .676 .771 95 458 660865 0960 1055 1150 1245 1.339 1434 1529 1623 1718 95 459 1813 1907 2002 2096 2191 228G 2380 247512569 2663! 95 1 . N. 1 1 1 1 2 1 3 ': 4 1 5 1 6 1 7 ! 8 1 9 I D. 1 A TABLE OF LOGARITHMS TEOISI 1 TO 10,000. N. 1 1 1 2 1 3 1 4 1 5 i 6 [ 7 ! 8 I 9 1 D. 1 460 662758 2852 2947 3041,3135 3230, 3324,3418 3512 3607 941 461 3701 3795 3SS9 39S3 4U78 4172 4266 4360 4454 4548 94 462 4642 4736 4830 4924 5018 5112 5200 5299 5393 5487 94 463 5581 5675 5769 5862 5956 6050 6143 6237 6331 6424 94 464 6518 6612 6705 6799 6892 6986 7079 7173 7266 7360 94 465 7453 7546 7640 7733 7826 7920 8013 8106 8i99 8293 93 466 8386 8479 8572 8665 8759 8S52 8945 9038 9131 9224 93 467 9317 9410 9503 9596 9689 9782 9J75 9967 ..60 .153 93 468 670241 0339 0431 0524 0617 OiiO: 0802 0895 0988 1080 93 469 1173 1265 1358 1451 1543 1636. 1728 1821 1913 2005 93 470 67209S 2190 2283 2375 2467 2560 2652 2744 2836 2929 92 471 ^•021 3113 3205 3297 3390 34S2; 3574 3666 3758 3850 92 472 3942 4034 4126 42 IS 4310 4402 4i94 4586 4677 4769 92 473 4861 4953 5045 5137 5228 5320: 5412 5503 5595 .5687 92 474 5778 5870 5962 6053 6 145 62361 6328 6419 6511 6602 92 475 6694 6785 6876 6968 7059 7151; 7242 7333 7424 7516 91 476 7607 7698 7789 76 81 7972 8063; 8154 8245 8336 8427 91 477 8518 8609 8700 8791 8SS2 89731 9064 9155 9246 9337 91 478 9428 9519 9610 9700 9791 98821 9973 ..63 .1.54 .245 91 479 680336 0426 0517 0607 0698 0789; 0879 0970 1060 1151 91 480 681241 1332 1422 1513 1603 16931 1784 1874 1964 2055 90 481 2145 2235 2326 2416 2506 2596 2686 2777 2867 2957 90 482 3047 3137 3227 3317 3407 3497 3587 3677 3767 3857 90 483 3947 4037 4127 4217 4307 4396 4486 4576 4666 4756 90 484 4845 4935 5025 5114 5204 5294 5383 5473 .5563 5652 90 485 5742 5831 5921 6010 6100 6189! 6279 6368 6458 6547 89 486 6636 6726 6815 6904 6994 7083i 7172 7261 7351 7440 89 487 7529 7618 7707 7796 7886 7975; 8064 8153 8242 8331 89 488 8420 8509 8598 8687 8776 8865^ 8953 9042 9131 9220 89 489 9309 9398 94S6 9575 9664 97 53i 9841 9930 ..19 .107 89 490 690196 0285 0373 0462 0550 0639; 0728 0816 0905 0993 89 491 1081 1170 125S 1347 1435 1524 1612 1700 1789 1877 88 492 1965 2053 2142 2230 2318 2406 ! 2494 2583 2671 2759 88 493 2847 2935 3023 3111 3199 3287: 3375 3463 3551 3639 88 494 3727 3815 3903 3991 4078 4166; 4254 4342 4430 4517 88 495 4605 4693 4781 4368 4956 5044; 5131 5219 5307 5394 88 496 5482 5569 5657 5744 5832 5919; 6007 6094 6182 6269 87 497 6356 6444 6531 6618 6706 67931 6880 6968 7055 7142 87 498 7229 7317 7404 7491 7578 7665: 7752 7839 7926 8014 87 499 8101 8188 8275 8362 8449 85351 8622 8709 8796 8883 87 500 698970 9057 9144 9231 9317 9404; 9491 9578 9664 9751 87 501 9838 9924 ..11 ..98 .184 .271j .358 .444 .531 .617 87 502 700704 0790 0877 0963 1050 11361 1222 1309 1395 1482 86 503 1568 1654 1741 1827 1913 1999; 2086 2172 2258 2344 86 504 2431 2517 2603 2689 2775 286 1: 2947 3033 3119 3205 86 505 3291 3377 3463 3549 3635 3721: 3S07 3895 3979 4065 86 506 4151 4236 4322 4408 4494 4579 4665 4751 4837 4922 86 507 5008 5094 5179 5265 5350 5436 5522 5607 5693 5778 86 508 5864 5949 6035 6120 6206 6291 6376 6462 6547 6632 85 509 510 6718 6803 7655 6888 7740 6974 7826 7059 7911 7144j2229 7996! 8081 7315 8166 7400 8251 7485 8336 85 85 707570 511 8421 8506 8591 8676 8781 8846; 8931 9015 9100 9185 85 512 9270 9355 9440 9524 9609 9694. 9779 9S63 9948 ..33 85 513 710117 0202 0287 0371 0456 05401 0625 0710 0794 0879 85 514 0963 1048 1132 1217 1301 1385) 1470 1554 1639 1723 84 515 1807 1892 1976 2060 2144 2229 2313 2397 24^1 2566 84 516 2650 2734 2818 2902 2986 3070 3154 3238 3323 3407 84 517 3491 3575 3650 3742 3S26 3910; 3994 4078 4162 4246 84 518 4330 4414 4497 4581 4665 47491 4833 4916 5000 5084 84 519 5167' 5251 5335! 5418 5502 55861 5669 5753' 58361 5920 84 JL 1 1 1 1 2 1 3 I 4 1 5 1 6 1 7 1 8 1 9 1 D. 1 A TABLE OF LOGARITHMS FROM I TO 10,000 9 TT" |l|2|3|4|6|6|7|8|9|D. 1 520 716003 6087. 6170 6254 7088 6337 6421 6504 6588 6671 6754 83 521 6838 6921 7004 7171 7254 7338 7421 7504 7587 83 522 7671 7754 7837 7920 8003 8086 8169 8253 8336 8419 83 523 8502 8585 8668 8751 8834 8917 9000 9083 9165 9248 83 524 9331 9414 9497 9580 9663 9745 9828 9911 9994 ..77 83 525 720159 0242 0325 0407 0490 0573 0655 0738 0821 0903 83 526 0986 1068 1151 1233 1316 1398 1481 1563 1646 1728 82 527 1811 1893 1975 2058 2140 2222 2305 2387 2469 2652 82 528 2634 2716 2798 2881 2963 3045 3127 3209 3291 3374 82 529 530 3456 724276 3538 4358 3620 4440 3702 4522 3784 4604 3866 4685 3948 4767 4030 4849 4112 4931 4194 82 82 5013 531 5095 5176 5258 5340 5422 5503 5585 5667 5748 5830 82 532 5912 5993 6075 6156 6238 6320 6401 6483 6564 6646 82 533 6727 6809 6890 6972 7053 7134 7216 7297 7379 7460 81 534 7541 7623 7704 7785 7866 7948 8029 8110 8191 8273 81 535 8354 8435 8516 8597 8678 8759 8841 8922 9003 9084 81 536 9165 9246 9327 9408 9489 9570 9651 9732 9813 9893 81 537 9974 ..55 .136 .217 .298 .378 .459 •540 .621 .702 81 538 730782 0863 0944 1024 1105 1186 1266 1347 1428 1608 81 539 1589 1669 1750 1830 1911 1991 2072 2152 2233 2313 81 540 732394 2474 2555 2635 2715 2796 2876 2966 3037 3117 80 541 3197 3278 3358 3438 3518 3598 3679 3769 3839 3919 80 542 3999 4079 4160 4240 4320 4400 4480 4560 4640 4720 80 543 4800 4880 4960 5040 5120 5200 5279 5359 6439 5619 80 544 5599 5679 5759 5838 5918 5998 6078 6157 6237 6317 80 545 6397 6476 6556 6635 6715 6795 6874 6954 7034 7113 80 546 7193 7272 7352 7431 7511 7590 7670 7749 7829 7908 79 547 7987 8067 8146 8225 8305 8384 8463 8543 8622 8701 79 548 8781 8860 8939 9018 9097 9177 9256 9335 9414 9493 79 549 550 9572 740363 9651 0442 9731 0521 9810 0600 9889 0078 9968 0757 ..47 0836 .126 .206 .284 79 79 0915 0994 1073 551 1152 1230 1309 1388 1467 1546 1624 1703 1782 1860 79 552 1939 2018 2096 2175 2254 2332 2411 2489 2668 2646 79 553 2725 2804 2882 2961 3039 3118 3196 3275 3363 3431 78 554 3510 3588 3667 3745 3S23 3902 3980 4058 4136 4216 78 555 4293 4371 4449 4528 4606 4684 4762 4840 4919 4997 78 556 . 5075 5153 5231 5309 5387 5465 5543 5621 5699 6777 78 557 5855 5933 6011 6089 6167 6245 6323 6401 6479 6656 78 558 6634 6712 6790 6868 6945 7023 7101 7179 7256 7334 78 559 560 7412 7489 8266 7567 8343 7645 8421 7722 8498 7800 8570 7878 8653 7955 8033 8808 8110 8886 78 77 748188 8731 561 8963 9040 9118 9195 9272 9350 9427 9504 9582 9659 77 562 9736 9814 9891 9968 ..45 .123 .200 .277 .364 .431 77 563 750508 0586 0663 0740 0817 0894 0971 1048 1126 1202 77 564 1279 1356 1433 1510 1587 1664 1741 1818 1896 1972 77 565 2048 2125 2202 2279 2356 2433 2509 2686 2663 2740 77 566 2816 2893 2970 3047 3123 3200 3277 3363 3430 3506 77 567 3583 3660 3736 3813 3889 3966 4042 4119 4195 4272 77 568 4348 4425 4501 4578 4654 4730 4807 4883 4960 5036 76 569 570 5112 5189 5951 5265 6027 5341 6103 5417 6180 5494 6256 5570 6332 6646 6408 5722 6484 5799 6560 76 76 765875 571 6636 6712 6788 6864 6940 7016 7092 7168 7244 7320 76 572 7396 7472 7548 7624 7700 7775 7851 7927 8003 8079 76 573 8155 8230 8306 8382 8458 8533 8609 8685 8761 8836 76 574 8912 8988 9063 9139 9214 9290 9366 9441 9517 9592 76 575 9668 9743 9819 9894 9970 ..45 .121 .196 .272 .347 75 576 760422 0498 0573 0649 0724 0799 0875 0950 1025 1101 75 577 1176 1251 1326 1402 1477 1552 1627 1702 1778 1853 75 578 1928 2003 2078 2153 2228 2303 2378 2453 2529 2604 75 579 2679 2754 2829 2904' 2978 3053 3128 3203 3278 3353 75 N. |ll2l3|4|5lfi!7i8l9|D. 1 B 10 A TAELE OF LOGARITHMS FIi03I 1 TO 10,000. 1 ^' 1 ilf2|3|4|5|6|7|8|9|D. 1580 763428 350S 5 3578, 3653, 3727, 3802, 3877 39521 40271 410] i 75 581 4176 4261 4326 44O0 4475 4550 4624 469£ ) 4774148481 75 682 4923 4998 5072 5147 5221 5296 5370 544c 552C 5594 ^ 75 583 6669 5742 5818 5892 5966 60411 6115 619( > 626"^ [ 6338 74 584 6413 648? 6562 6636 6710 67851 6859 693£ 7007 ' 7082 74 585 7156 7230 7304 7379 7453 7527! "^601 767£ 774S 7823 74 686 7898 7972 8046! 8120 8194 8268: 8342 8416 849C 8564 74 587 8638 8712 87861 8860 8934 9008 i 9082 9156 |9230 9303 74 588 9377 9451 9525| 9599 9673 9746i 9820 19894 996S ..42 74 689 590 770115 770852 0189 0263 j 0336 09991 1073 |0410 1 1146 0484! 0557 1220; 1293 0631 1367 ! 0705 1 1440 0778 ; 1514 74 74 0926 591 1687 1661 173"^ y 1808J 1881 1955; 2028 2102 12175 ,2248 73 692 2322 2395 2468 ] 2542 2615 2688: 2762 2835 12908 i 2981 73 693 3055 3128 320] 3274 3348 342113494 3567 i 3640 |3713 73 694 3786 3860 3932 1 4006 4079 4152 4225 4298 ; 4371 '4444 73 595 4517 4590 46631 4736 4809 4882! 4955 6028 |5100 |5173 73 596 5246 5319 5392! 5465 5533! 56101 56831 5756 5829 5902 73 697 6974 6047 612016193 6265| 6338 6411 6483 6556 6629 73 598 6701 6774 68461 6919 69921 7064i 7137 7209 ! 7282 7354 73 599 7427 7499 75721 7644 7717i 7789! 7862 7934 8006 8079 72 600 778151 8224 8296i 83681' 8441 1 85131 85851 8G58 8730 8802 72 601 8874 8947 90191 90911 91631 92361 9308| 9380 9452 9524 72 602 9596 9669 974l!9S13 9885! 9957! .•29! .101 .173 .245 72 l603 780317 0389 0481! 0533 0605 0677| 0749! 0821 0893 0965 72 604 1037 1109 1181 1253 1324 13961 1468! 1640 1612 1684 72 605 1755 1827 1899 1971 20421 21l4i 2186 2258 2329 2401 72 606 2473 2544 2616^ 2688 2759! 2831; 2902] 2974 3046 3117 72 607 3189 3260 33321 3103 3475 3546, 36iS| 3689 3761 3832 71 608 3904 3975 4046 4118 4189 4261) 4332! 4403 4475 4546 71 609 4617 4689 476^^1 4S3i 49021 4974' 5045! 5116 5187 5259 71 610 ? 85330 j 6401 54721 6543 56l5j 5686! 5757J 5828 5899 5970 71 611 6041 6112 6183, 6254 6325] 6396! 6467 6538 6609 6680 71 612 6751 6822 6893 69641 7035 7106! 7177| 7248 7319 7390 71 613 7460 7531 7602 7673 7744! 7815 78851 7956 8027 8098 71 614 8168 8239 8310 8381 8451 -8522 8593' 8663 8734 8804 71 615 8875 8946 3016 9087 9167 9228 9299i 9369 9440 9510 71 616 9581 9651 9722 9792 9863 9933 ...4] ..74 .144 .215 70 617 790285 0356 0426 0496 0567 0637 0707] 0778 0848 0918 70 618 0988 1059 1129 1199 12691 1340 1410! 1480 1550 1620 70 619 620 1691 1761 1831 2532 19011 1971 2041 26021 2672| 2742 2II1I 2181 2812 2S82 2252 2952 2322 70 70 792392 2462 3022] 621 3092 3162 3231 3301 3371 3441 3511 3581 3651 3721 70 022 3790 3860 3930 4000 4070 4139 4209 4279 4349 4418 70 623 4488 4558 4627 4697 4767i 4836 4906, 4976 5045! 5115 70 624 6185 5254 5324 5393 54631 5532 6602! 56721 5741! 5811 70 625 5880 5949 6019 6088 6158! 6227 6297 6366| 6436! 6505 69 626 6574 6644 6713 6782 6852! 6921 6990 7060| 7129 7198 69 627 7268 7337 7406 7475, 75451 7614 7683 7752] 7821! 7890 69 628 7960 8029 8098 8167 8236] 8305 8374 84431 8513 8582 69 639 630 1 8651 8720 8789 8358 &927i 8996 96161 9685 9065 9134 9823 9203 9272 9961 69 69 799341 9409 9478 9547 9754 9892 631 800029 0098 0167 0236 0305! 0373 0442 0511 0680 0648 69 632 0717 0786 0854 0923 09921 1061 112& 1198 1266 1335 69 633 1404 1472 1541 1609 1678J 1747 1815 1884 1952 2021 69 634 2089 2168 2226 2295 2363: 2432 2500 2568 2637 2705 69 636 2774 2842 2910 2979 3047 3116 3184 32521 3321 3389 68 636 34571 3525 3594 3862] 37301 3798 3867 3935 4003 4071 68 637 4139 4208 4276 4344 4412.' 4480 4548 4616 4685 4763 68 638 4821 4889 4957 5025 5093; 5161 5229 5297J 5365 5433 68 639 5501 5569 5637 5705 57731 5841 59081 59761 6044 6112 68 1 JM |l|2|3|4|5|6|7|8!9|D. f A TABLE OF LOGARITHMS FROM 1 TO 10,000. 11 N. l|2|3|4|5l6|7|8|9|D. 1 640 806180 6248 63161 6384 6451 6519 6587 6655 67231 6790 68 B41 6858 6926 6994 7061 7129 7197 7264 7332 7400 7467 68 642 7535 7603 7670 7738 7806 7873 7941 8008 8076 8143 68 643 8211 8279 8346 8414 8481 8549 8616 8684 8751 8818 67 644 8886 8953 9021 9088 9156 9223 9290 9358 9425 9492 67 645 9580 9627 9094 9762 9829 9896 9964 ..31 ..98 .165 67 646 810233 0300 0367 0434 0501 0569 0636 0703 0770 0837 67 647 0904 0971 1039 1106 1173 1240 1307 1374 1441 1508 67 648 1575 1642 17091 1776 1843 1910 1977 2044 2111 2178 67 649 650 2245 2312 2980 2379 3047 2445 3114 2512 3181 2579 3247 2646 3314 2713 3381 2780 3448 2847 3514 67 67 812913 651 3581 3648 3714 3781 3S48 3914 3981 4048 4114 4181 67 652 4248 4314 4381 4447 4514 4581 4647 4714 4780 4847 67 653 4913 4980 5046 5113 5179 5246 5312 5378 5445 .5511 66 654 5578 5644 5711 5777 5843 5910 5976 6042 6109 6175 66 655 6241 6308 6374 6440 6506 6573 6639 6705 6771 6838 66 656 6904 6970 7036 7102 7169 7235 7301 7367 7433 7499 66 657 7565 7631 7698 7764 7830 7896 7962 8028 8094 8160 66 658 8226 8292 8358 8424 8490 8556 8622 8688 8754 8820 66 659 8885 8951 9017 9083 9149 9215 9281 9346 9412 9478 66 660 819544 9610 9676 9741 9807 9873 9939 ...4 ..70 .136 66 661 820201 0267 0338 0399 0464 0530 0595 0661 0727 0792 66 662 0858 0924 0989 1055 1120 1186 1251 1317 1382 1448 66 663 1514 1579 1645 1710 1775 1841 1906 1972 2037 2103 65 664 2168 2233 2299 2364 2430 2495 2560 2626 2691 2756 65 665 2822 2887 2952 3018! 3083 3148 3213 3279 3344 3409 65 666 3474 3539 3605 3670 3735 3800 3865 3930 3996 4061 65 667 4126 4191 4256 4321 4386 4451 4516 4581 4646 4711 65 668 4776 4841 4906 4971 5036 5101 5166 5231 5296 5361 65 669 5426 5491 5556 5621 5686 5751 5815 5880 5945 6010 65 670 826075 6140 6204 6269 6334 6399 6464 6528 6593 6658 65 671 6723 6787 6852 6917 6981 7046 7111 7175 7240 7305 65 672 7369 7434 7499 7563 7628 7692 7757 7821 7886 7951 65 G73 8015 8080 8144 8209 8273 8338 8402 8467 8531 8595 64 674 8660 8724 8789 8853 8918 8982 9046 9111 9175 9239 64 675 9304 9368 9432 9497 9561 9625 9690 9754 9818 9882 64 676 9947 ..11 ..75 .139 .204 .288 .332 •396 .460 .525 64 677 830589 0653 0717 0781 0845 0909 0973 1037 1102 1166 64 678 1230 1294 1358 1422 1486 1550 1614 1678 1742 1806 m 679 680 1870 1934 2573 1998 2637 2062 2700 2126 2764 2189 2828 2253 2892 2317 2958 2381 3020 2445 3083 64 64 832509 681 3147 3211 3275 3338 3402 3466 3530 3593 3657 3721 64 682 3784 3848 3912 3975 4039 4103 4166 4230 4294 4357 64 683 4421 4484 4548 4611 4675 4739 4802 4866 4929 4993 64 684 5056 5120 5183 5247 5310 5373 5437 5500 5564 5627 63 685 5691 5754 5817 5881 5944 6007 6071 6134 6197 6261 63 686 6324 6387 6451 6514 6577 6641 6704 6767 6830 6894 63 687 6957 7020 7083 7146 7210 7273 7336 7399 7462 7525 63 688 7588 7652 7715 7778 7841 7904 7967 803C 8093 81.56 63 689 8219 8282 8345 8408 8471 8534 8597 8660 8723 8786 63 690 838849 8912 8975 9038 9101 9164 9227 9289 9352 9415 63 691 9478 9541 9604 9667 9729 9792 9855 9918 9981 ..4:^ 63 692 840106 0169 0232 0294 0357 0420 0482 0.545 0608 0671 63 693 0733 0796 0859 0921 0984 1046 1109 1172 1234 T297 63 694 1359 1422 1485 1547 1610 1672 1735 1797 1860 1922 63 695 1985 2047 2110 2172 2235 2297 2360 2422 2484 2547 62 696 2609 2672 2734 2796 2859 2921 2983 3046 3108 3170 62 697 3233 3295 3357 3420 3482 3544 3606 3669 .3731 3793 ^62 698 3855 3918 3980 4042 4104 4166 4229 4291 4353 4415 <-62 699 4477 4539 4601 4664 4726 4788 4850 4912 4974 5036 62 t N. I |I|2|3|4|5|6|7|8|9|D. 1 12 A TABLE OF lOGARITHSIS FKOM 1 TO 1 o,ooc , N. 1 ! 1 1 2 1 3 1 4 I 5 1 6 1 7 1 8 1 9 1 D. 1 700 845098 5160 5222 5284 5346 5408 1 5470 5532 5594 5656i 62 1 701 5718 5780 5842 5904 5966 6028 6090 6151 6213 6275 62 702 6337 6399 6461 6523 6585 6646 6708 6770 6832 6894 62 703 6955 7017 7079 7141 7202 7264 7320 7388 7449 7511 62 704 7573 7634 7696 7758 7819 7881 7943 8004 8066 8128 62 705 8189 8251 8312 8374 8435 8497 8559 8620 8682 8743 62 706 8805 8866 8928 8989 9051 9112 9174 9235 9297 9358 61 707 9419 9481 9542 9604 9665 9726 9788 9849 9911 9972 61 708 850033 0095 0156 0217 0279 0340 0401 0462 0524 0585 61 709 710 0646 851258 0707 1320 0769 0830 0891 0952 1014 1625 1075 1136 1747 1197 1809 61 61 1381 1442 1503 1564 1686 711 1870 1931 1992 2053 2114 2175 2236 2297 2358 2419 61 712 2480 2541 2602 2663 2724 2785 2846 2907 2968 3029 61 713 3090 3150 3211 3272 3333 3394 3455 35 1 6 3577 ,3637 61 714 3698 3759 3820 3881 3941 4002 4063 4124 4185 4245 61 715 4306 4367 4428 4488 4549 4610 4670 4731 4792 4852 61 716 4913 4974 5034 5095 5156 5216 5277 5337 5398 5459 61 717 5519 5580 5640 5701 5761 5822 5882 5943 6003 6064 61 718 6124 6185 6245 6306 6366 6427 6487 6548 6608 6668 60 719 720 6729 857332 6789 6850 6910 7513 6970 7031 7634 7091 7694 7152 7212 7815 7272 60 60 7393 7453 7574 7755 7875 721 7935 7995 8056 8116 8176 8236 8297 8357 8417 8477 60 722 8537 8597 8657 8718 8778 S838 8898 8958 9018 9078 60 723 9138 9198 9258 9318 9379 9439 9499 9559 9619 9679 60 724 9739 9799 9859 9918 9978 ..38 ..98 .158 .218 .278 60 725 860338 0398 0458 0518 0578 0637 0697 0757 0817 0877 60 726 0937 0996 1056 1116 1176 1236 1295 1355 1415 1475 60 727 1534 1594 1654 1714 1773 1833 1893 1952 2012 2072} 601 728 2131 2191 2251 2310 2370 2430 2489 2549 2608 2668 60 729 '730 2728 2787 2847 2906 3501 2966 3025 3620 3085 3144 3739 3204 3799 3263 3358 60 59 863323 3382 3442 3561 3080 731 3917 3977 4036 4096 4155 4214 4274 4333 4392 4452 59 732 4511 4570 4630 4689 4748 4808 4867 4926 4985 5045 59 733 5104 5163 5222 5282 5341 5400 5459 5519 5578 5637 69 734 5696 5755 5814 5874 5933 5992 6051 6110 6169 6223 59 735 6287 6346 6405 6465 6524 6583 6642 6701 6760 6819 59 736 6878 6937 6996 7055 7114 7173 7232 7291 7350 7409 59 737 7467 7526 7585 7644 7703 7762 7821 7880 7939 7998 59 738 8056 8115 8174 8233 8292 8350 8409 8468 8527 8586 59 739 740 8644 8703 9290 8762 8821 8879 9466 8938 9525 8997 9056 9114 9173 9760 59 59 869232 9349 9408 9584 9642 9701 741 9818 9877 9935 9994 ..53 • 111 .170 .228 .287 .345 59 742 870404 0462 0521 0579 0638 0696 0755 0813 0872 0930 58 743 0989 1047 1106 1164 1223 1281 1339 1398 1456 1515 58 744 1573 1631 1690 1748 1806 1865 1923 1981 2040 2098 58 745 2156 2215 2273 2331 2389 2448 2506 2564 2622 2681 58 746 2739 2797 2855 2913 2972 3030 3088 3146 3204 3262 58 747 3321 3379 3437 3495 3553 3611 3669 3727 3785 3844 58 748 3902 3960 4018 4076 4134 4192 4250 4308 4366 4424 58 749 750 4482 4540 4598 4656 4714 5293 4772 5351 4830 5409 4888 5466 4945 5524 5003 5582 58 58 875061 5119 5177 5235 751 5640 5698 5756 5813 5871 5929 5987 6045 6102 6160 58 752 6218 6276 6333 6391 6449 6507 6564 6622 6680 6737 58 753 6795 6853 6910 6968 7026 7083 7141 7199 7256 7314 58 754 7371 7429 7487 7544 7602 7659 7717 7774 7832 7889 58 755 7947 8004 8062 8119 8177 8234 8292 8349 8407 8464 57 756 8522 8579 8637 8694 8752 8809 8866 8924 8981 9039 57 757 9096 9153 9211 9268 9325 9383 9440 9497 9555 9612 67 758 9669 9726 9784 9841 9898 9956 ..13 ..70 .127 .185 67 759 880242 0299103561 0413 0471 0528 05851 0642 0699 0756 57 N. 1 |l|2|3|4|5|6|7i8|9!D. 1 A TABLE OF LOGAEITHMS FROM 1 TO IC ),000 13 N. 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 ! D. 1 760 880814.0871, 0928 0985 1042 1099 1156 1213 1271 1328 67 761 1385 1442 1499 1556 1613 1670 1727 1784 1841 1898 57 762 1955 2012 2069 2126 2183 2240 2297 2354 2411 2468 57 763 2525 2581 2638 2695 2752 2809 2866 2923 2980 3037 57 764 3093 3150 3207 3264 3321 3377 3434 3491 3548 3605 67 765 3661 3718 3775 3832 3888 3945 4002 4059 4116 4172 57 766 4229 4285 4342 4399 4455 4512 4569 4625 4682 4739 57 767 4795 4852 4909 4965 5022 5078 5135 5192 5248 6305 57 768 5361 5418 5474 5531 5587 5644- 5700 5757 5813 6870 57 769 770 5926 5983 6039 6096 6152 6716 6209 6265 6321 6378 6434 56 66 886491 ! 6547 6604 6660 6773 6829 6885 6942 6998 771 70541 7111 7167 7223 7280 7336 7392 7449 7506 7561 66 772 7617 7674 7730 7786 7842 7898 7955 8011 8067 8123 66 773 8179 8236 8292 8348 8404 8460 8516 8573 8629 8686 56 774 8741 8797 8853 8909 8965 9021 9077 9134 9190 9750 9246 66 775 9302 9358 9414 9470 9526 9582 9638 9694 9806 66 776 98621 9918 9974 ..30 ..86 .141 .197 .253 .309 .365 56 777 890421 0477 0533 0.589 0645 0700 0756 0812 0868 0924 66 778 0980 1035 1091 1147 1203 1259 1314 1370 1426 1482 66 779 780 1537 892095 1593 1649 2206 1705 2262 1760 2317 1816 2373 1872 2429 1928 1983 2039 56 66 2150 2484 2540 2595 781 2651 2707 2762 2818 2873 2929 2985 3040 3096 3161 56 782 3207 3262 3318 3373 3429 3484 3540 3595 3651 3706 56 783 3762 3817 3873 3928 3984 4039 4094 4150 4205 4261 66 784 4316 4371 4427 4482 4538 4593 4648 4704 4759 4814 55 785 4870 4925 4980 5036 5091 5146 6201 6257 5312 6367 66 786 5423 5478 5533 5588 6644 5699 5754 .5809 5864 5920 66 787 6975 6030 6085 6140 6195 6251 6306 6361 6416 6471 66 788 6526 6581 6636 6692 6747 6802 6857 6912 6967 7022 66 789 790 7077 897627 7132 7187 7242 7297 7352 7407 7462 7517 7572 65 66 7682 7737 7792 7847 7992 7957 8012 8067 8122 791 8176 8231 8286 8341 8396 8451 8606 8561 8615 8670 56 792 8725 8780 8835 8890 8944 8999 9054 9109 9164 9218 66 793 9273 9328 9383 9437 9492 9547 9602 9656 9711 9766 66 794 98211 9875 9930 9985 ..39 ..94 .149 .203 .258 .312 65 795 900367] 0422 0476 0531 0586 0640 0695 0749 0804 0859 56 T96 0913i 0968 1022 1077 1131 1186 1240 1295 1349 1404 65 797 1458 1513 1567 1622 1676 1731 1785 1840 1894 1948 64 798 2003 2057 2112 2166 2221 2275 2329 2384 2438 2492 54 799 800 2547 2601 2655 2710 2764 3307 2818 2873 2927 3470 2981 3524 3036 3678 54 64 903090 3144 3199 3253 3361 3416 801 3633 3687 3741 3795 3849 3904 3958 4012 4066 4120 54 802 4174 4229 4283 4337 4391 4445 4499 4653 4607 4661 54 803 4716 4770 4824 4878 4932 4986 5040 5094 6148 6202 54 804 5256 5310 5364 .5418 5472 5526 5580 6634 6688 6742 54 805 5796 5850 5904 5958 6012 6066 6119 6173 6227 6281 64 806 6335 6389 6443 6497 6551 6604 6658 6712 6766 6820 54 807 6874 6927 6981 7035 7089 7143 7196 7250 7304 7368 64 806 7411 7465 7519 7573 7626 7680 7734 7787 7841 7895 64 809 810 7949 908485 8002 8539 8056 8592 8110 8163 8217 8270 8324 8378 8914 8431 8967 64 54 8646 8699 8753 8807 8860 811 9021 9074 9128 9181 9235 9289 9342 9396 9449 9603 64 812 9556 9610 9663 9716 9770 9823 9877 9930 9984 ..37 53 813 910091 0144 0197 0251 0304 0358 0411 0464 0518 0571 63 814 0624 0678 0731 0784 0838 0891 0944 0998 1051 1104 63 815 1158 1211 1264 1317 1371 1424 1477 1 630 1.584 16.37 63 816 1690 1743 1797 1850 1903 1956 2009 2063 2116 2169 63 81Y 2222 2275 2328 2381 2435 2488 2541 2694 2647 2700 63 818 2753 2806 2859 2913 2966 3019 3072 3125 3178 3231 63 819 3284 3337 3390 3443 3496 3549 13602 3655 3708 3761 63 N. i ll|2|3|4!5|6l7i8|9|D. 1 14 A TABLE OF LOGARITHMS FBOM 1 TO 10,000. "n. 1 1 ' 2 ' 3 ! 4' 5 ! 6 I 7 ; 8 i 9 D. | '820 9 138 14 3S67 3920 3973 4026 4079 4132 41S4 4237 4290 53 821 4343 4396 4449 4502 4555 4608 4660 4713 4766 4819 53 822 4S72 4925 4977 5030 50S3 5136 51S9 5241 5294 5347 53 823 5400 5453 5505 5558 5611 5664 5716 5769 5822 5375 53 824 5927 59S0 6033 6085 6138 6191 6243 6296 6349 6401 53 825 6454 6507 6559 6612 6664 6717 6770 6822 6875 6927 53 826 6980 7033 7085 7138 7190 7243 7295 7348 7400 7453 53 827 7506 755S 7611 7663 7716 776S 7320 7873 7925 7978 52 828 8030 S0S3 8135 S13S 8240 8293 8345 8397 8450 8502 52 829 8555 S607 8659 S 7 i 2 8764 SS16 8869 S921 8973 9026 52 830 919078 9130 91 S3 9235 92S7 9340 9392 9444 9496 9549 52 831 96011 9653 9706 975S 9S10 9S62 9914 9967 ..19 ..71 52 S32 920123 0176 022^ 0230 0332 03S4 0436 0489 0541 0593 52 833 0645 0697 0749 OSOl OS 53 0906 0958 1010 1062 1114 52 834 1168 121S 1270 1322 1374 1426 147S 1530 1582 1634 52 835 16S6 173S 1790 1S42 1S94 1946 1993 2050 2102 21.54 52 836 2206 2258 2310 2362 2414 2466 2518 2570 2622 2674 52 837 2725 2777 2.^29 2^81 2933 2985 3037 3089 3140 3192 52 838 3244 3296 3348 3399 3451 3503 3555 3607 3658 3710 52 839 3762 3S14 3S65 3917 3969 4021 4072 4124 4176 4228 52 840 924279 4331 43S3 4.434 44S'^ 45 33 45 S 9 4641 4693 4744 52 841 4796 4348 4S99 4951 5003 5054 5108 5157 5209 5261 52 842 5312 5364 5415 5467 5518 5570 5621 5673 5725 5776 52 843 5828 '5879 5931 59S2 6034 6085 6137 6188 6240 6291 51 844 6342 6394 6-U5 6497 654S 6600 6651 6702 6754 6805 51 845 6857 690S 6959 7011 7062 7114 7165 7216 7268 7319 51 846 7370 7422 7473 7524 7578 7627 7678 7730 7781 7832 51 847 7383 7935 79S5 S037 8088 8140 8191 S242 8293 8345 51 848 8396 8447 8498 S549 8601 8652 8703 8754 8805 8S57 51 849 8908 8959 9010 9061 9112 9163 9215 9266 9317 9368 51 850 929419 9470 9521 9572 9623 9674 9725 9776 9S27 9S79 51 851 9930 9981 .,32 ..83 .134 .185 .236 .287 .338 .389 51 852 930440 0491 0542 0592 0643 0694 0745 0796 0847 0893 51 853 0949 1000 1051 1102 1153 1204 1254 1305 1356 1407 51 854 1458 1509 1560 1610 1661 1712 1763 1814 1865 1915 51 855 1966 2017 2068 2118 2169 2220 2271 2322 2372 2423 51 856 2474 2524 2575 2626 2877 2727 2778 2829 2879 2930 51 857 2981 3031 30 S 2 3133 3183 3234 3285 3335 33S6 3437 51 858 3487 353S 35S9 3639 3690 3740 3791 3841 3392 3943 51 859 3993 4044 4094 4145 4195 4246 4296 4347 4397 4443 51 860 93449S 4549 4599 4650 4700 4751 4S01 4S52 4902 4953 50 861 5003 5054 5104 5154 5205 5255 5306 5356 5406 5457 50 862 5507 5558 5603 5653 5709 5759 5S09 5S60 5910 5960 50 863 6011 6081 6111 6162 6212 6262 6313 6363 6413 6463 50 864 6514 6564 6614 6665 6715 6765 68 15 6865 6916 6966 50 865 7016 7066 7117 7167 7217 7267 7317 7367 7418 7468 50 866 7518 7568 76 IS 7663 7718 7769 7819 7869 7919 7969 50 867 8019 8069 8119 8169 8219 8269 8320 8370 S420 8470 50 868 8520 8570 8620 8670 8720 8770 8S20 8870 8920 8970 50 869 9020 9070 9120 9170 9220 9270 9320 9369 9419 9469 50 870 939519 9569 9619 9669 9719 9769 9S19 9S69 9918 9968 50 871 940018 006S Oil* 016S 021S 0267 0317 0367 0417 0467 50 872 0516 0566 0616 0666 0716 0765 OS 15 0865 0915 0964 50 873 1014 1064 1114 1163 1213 1263 1313 1362 1412 1462 50 874 1511 1561 1611 1660 1710 1760 1S09 1S59 1909 1958 50 875 200S 205S 2107 2157 2207 2256 2306 2355 2405 24.55 50 876 250-i 2554 2603 2653 2702 2752 2801 285 1 2901 2950 50 -877 3000 3049 3099 3148 3198 3247 3297 3346 3396 3445 49 878 3495 3544 3593 3643 3692 3742 3791 3S41 3S90 3939 49 879 39S9 4038^ 4088 4137 4186 4236 4235 4335 43S4 4433' 49 J N. i 1 1 1 2 1 3 1 4 i 5 6 7 8 9_ ^ A TABLE OF LOGARITHMS FRO^l 1 TO 10,000. 15 N. 1 |l|2|3|4|5|6|7|8|9| D.( 880 944483 4532 4581 46311 4680 4729 4779 4828 4877 4927 49 SHI 4976 5025 5074 5124 5173 5222 5272 5321 5370 5419 49 882 5469 5518 5567 5616 5665 5715 5764 5813 5862 5912 49 883 5961 6010 6059 6108 6157 6207 6256 6305 6354 6403 49 884 6452 6501 6551 6600 6649 6698 6747 6796 6845 6894 49 885 6943 6992 7041 7090 7140 7189 7238 7287 7336 V38b 49 886 7434 7483 7532 7581 7630 7679 7728 7777 7826 7875 49 887 7924 7973 8022 8070 8119 8168 8217 8266 8315 8364 49 888 8413 8462 8511 8560 8609 8657 8706 8755 8804 8853 49 889 890 8902 8951 9439 8999 9488 9048 9536 9097 9585 9146 9634 9195 9683 9244 9731 9292 9780 9341 9829 49 49 949390 891 9878 9926 9975 ..24 ..73 .121 .170 .219 .267 .316 49 892 950365 0414 0462 0511 0560 0608 0657 0706 0754 0803 49 893 0851 0900 0949 0997 1046 1095 1143 1192 1240 1289 49 894 1338 1386 1435 1483 1532 1580 1629 1677 1V26 1775 49 895 1823 1872 1920 1969 2017 2066 2114 2163 2211 2260 48 896 2308 2356 2405 2453 2502 2550 2599 2647 2696 2744 48 897 2792 2841 2889 2938 2986 3034 3083 3131 3180 3228 48 898 3276 3325 3373 3421 3470 3518 3566 3615 3663 3711 48 899 900 3760 3808 4291 3856 4339 3905 4387 3953 U35 4001 4484 4049 4532 4098 4580 4146 4628 4194 4677 48 48 954243 901 '4725 4773 4821 4869 4918 4966 5014 5062 5110 5158 48 902 5207 5255 5303 5.351 5399 5447 5495 5543 5592 5640 48 903 5688 5736 5784 .5832 5880 5928 5976 6024 6072 6120 48 904 6168 6216 6285 6313 6361 6409 6457 6505 6553 6601 48 905 6649 6697 6745 6793 6840 6888 6936 6984 7032 7080 48 906 712S 7176 7224 7272 7320 7368 7416 7464 7512 7559 48 907 7607 7655 7703 7751 7799 7847 7894 7942 7990 8038 48 908 8086 8134 8181 8229 8277 8325 8373 8421 8468 8516 48 909 910 8564 8612 9089 8659 9137 8707 9185 8755 9232 8803 9280 8850 9328 8898 9375 8946 9423 8994 9471 48 48 959041 911 9618 9566 9614 9661 9709 9757 9804 9852 9900 9947 48 912 9995 ..42 ..90 .138 .185 .233 .280 .328 .376 .423 48 913 960471 0518 0566 0613 0661 0709 0756 0804 0851 0899 48 914 0946 0994 1041 1089 1136 1184 1231 1279 1326 1374 47 915 1421 1469 1516 1563 1611 1658 1706 1753 1801 1848 47 916 1895 1943 1990 2038 2085 2132 2180 2227 2275 2322 47 917 2369 2417 2464 2511 2559 2606 2653 2701 2748 2795 47 918 2843 2890 2937 2985 3032 3079 3126 3174 3221 3268 47 919 920 3316 963788 3363 3835 3410 3882 3457 3929 3504 3977 3552 3599 3646 4118 3693 4165 3741 4212 47 47 4024 4071 921 4260 4307 4354 4401 4448 4495 4542 4590 4637 4684 47 922 4731 4778 4825 4872 4919 4966 5013 .5061 5108 5155 47 923 5202 5249 5296 5343 5390 5437 5484 5531 5578 5625 47 924 5672 5719 5766 5813 .5860 5907 5954 6001 6048 6095 47 925 6142 6189 6236 6283 6329 6376 6423 6470 6517 6.564 47 926 6611 6658 6705 6752 6799 6845 6892 6939 6986 7033 47 927 7080 7127 7173 7220 7267 7314 7361 7408 7454 7501 47 928 7548 7595 7642 7688 7735 7782 7829 7875 7922 7969 47 929 930 8016 8062 8.530 8109 8576 8156 8623 8203 8670 8249 8716 8296 8763 8343 8810 8390 8856 8436 8903 47 47 968483 931 8950 8996 9043 9090 9136 9183 9229 9276 9323 9369 47 932 9416 9463 9509 9556 9602 9649 9695 9742 9789 9835 47 933 9882 9928 9975 ..21 ..68 AU .161 .207 .2.54 .300 47 934 970347 0393 0440 0486 0533 0579 0626 0672 0719 0765 46 935 0812 0858 0904 0951 0997 1044 1090 1137 1183 1229 46 936 1276 1322 1369 1415 1461 1508 1.554 1601 1647 1693 46 937 1740 1786 1832 1879 1925 1971 2018 2064 2110 2157 46 938 2203 2249 2295 2342 2388 2434! 2481 2.527 2573 2619 46 939 26661 2712' 2758 2804 2851 2897' 2943 2989 3035 3082' '46 1 N. 1 |l|2|3|4l5|6|7|8|9|D. 1 16 A TAELE OF LOGARITHMS FBOM 1 TO 10.000. N. |li2i3i4'5!6;7!8!9|D. j 940 97312S 317-i 3220 3C66 3313 3359 3405 3451' 3497 3543 46 941 3590 3636 36S2 3728 3774 3820 3866 3913 3959 4005 46 942 4051 4097 4143 4189 4235 4281 4327 4374 4120 4466 46 943 4512 4558 4604 4650 4696 4742 4788 4834 4880 4926 46 944 4972 5018 5064 5110 5156 5202 5248 5294 5340 5386 46 945 5432 5478 5524 5570 5616 5662 5707 5753 5799 5845 46 946 6891 5937 5983 6029 6075 6121 6167 6212 6258 6304 45 947 6350 6396 6442 64S8 6533 6579 6625 6671 6717 6763 46 948 6808 6854 6900 6948 6992 7037 7033 7129 7175 7220 46 949 7266 7312 7358 7403 7-U9 7495 7541 7586 7632 7678 46 950 977724 7769 7815 7861 7906 7952 7998 8043 3089 8135 46 951 8181 8226 8272 8317 8363 S409 3454 8500 8546 8591 46 953 8637 8683 S728 8774 8819 8865 8911 8956 9002 9047 46 953 9093 9138 9184 9230 9275 9321 9366 9412 9457 9503 46 954 9548 9594 9639 9685 9730 9776 9821 9867 9912 9958 46 955 980003 0049 0094 0140 0185 0231 0276 0322 0367 0412 45 956 0458 0503 0549 0594 0640 0685 0730 0776 0821 0367 45 957 0912 0957 1003 1048 1093 1139 1184 1229 1275 1320 45 958 1366 1411 1456 1501 1547 1592 1637 1633 1728 1773 45 959 960 1819 1864 2316 1909 2362 1954 2407 2000 2452 2045 2497 2090 2543 2135 2588 2181 2633 2226 2678 45 45 982271 961 2723 2769 2814 2859 2904 2949 2994 3040 3085 3130 45 962 3175 3220 3265 3310 3356 3401 3446 3491 3536 3581 45 963 3626 3671 3716 3762 3807 3852 3897 3942 3987 4032 45 964 4077 4122 4167 4212 4257 4302 4347 4392 4437 44S2 45 965 4527 4572 4617 4662 4707 4752 4797 4842 4887 4932 45 966 4977 5022 5067 5112 5157 5202 5247 5292 5337 5382 45 967 5426 5471 5516 5561 5606 5651 5696 5741 5786 5330 45 968 5875 5920 5985 6010 6055 6100 6144 6189 6234 6279 45 969 6324 6339 6413 645S 6503 654S 6593 6637 66S2 6727 45 970 986772 6817 6861 6906 6951 6996 7040 7035 7130 7175 45 971 7219 7264 7309 7353 7398 7443 7438 7532 7577 7622 45 972 7666 7711 7756 7S00 7845 7890 7934 7979 8024 8068 45 973 8113 8157 S202 8247 8291 8336 8381 8425 8470 8514 45 974 8559 8604 8648 8693 8737 ■8782 3826 8871 8916 8960 45 975 9005 9049 9094 9138 9183 9227 9272 9316 9361 9405 45 976 9450 9494 9539 9583 9828 9672 9717 9761 9806 9850 -44 977 9895 9939 99S3 ..28 ..72 .117 .161 .206 .250 .294 44 978 990339 0333 0428 0472 0516 0561 0605 0650 0694 0733 44 979 0783 0827 0871 0915 0960 1004 1049 1093 1137 1182 44 9S0 991226 1270 1315 1359 1403 1443 1492 1536 1580 1625 44 981 1669 1713 1758 1802 1846 1890 1935 1979 2023 2067 44 982 2111 2156 2200 2244 2288 2333 2377 2421 2465 2509 44 983 2554 2593 2642 2636 2730 2774 2819 2863 2907 2951 44 984 2995 3039 3083 3127 3172 3216 3260 3304 3348 3392 44 985 3436 3480 3524 3568 3613 3657 3701 3745 3789 3333 44 986 3877 3921 3965 4009 4053 4097 4141 4185 4229 4273 44 987 4317 -4361 4405 4449 4493 4537 4581 4625 4669 4713 44 988 4757 4301 4S45 4889 4933 4977 5021 5065 5108 5152 44 989 5196 5240 5284 5328 5372 5416 5460 5504 5547 5591 44 990 995635 5679 5723 5767 5811 5854 5898 5942 5986 6030 44 991 6074 6117 6161 6205 6249 6293 6337 6380 6424 6468 44 992 6512 6555 6599 6643 6687 6731 6774 6818 6862 6906 44 993 6949 6993 7037 7080 7124 7168 7212 7255 7299 7343 44 994 73S6 7430 7474 7517 7561 7605 7648 7692 7736 7779 44 995 7823 7867 7910 7954 7998 8041 8085 8129 8172 8216 44 996 8259 8303 8347 8390 8434 8477 8521 8564 8608 8652 44 997 8695 8739 8782 S826 8869 8913 8956 9000 9043 9087 44 998 9131 9174 9218 9261 9305 9348 9392 9435 9479 9522 44 999 9565 9809 9652 960F. 9739 9783 9826 98 70! 9913 9957 43 N. 1 |l|2|3i4|5i6i7|8!9|D. I A TABLE OF LOGARITHMIC SINES AND TANGENTS, FOR EVERY DEGREE AND MINUTE OP THE QUADRANT. N.B. The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right-hand column, belong to the degrees below. ^18 ( Degree.) a tab] LE or LOG ARITHMIC M. 1 Sine 1 D. C -aiue 1 D. Tang. D Cotan;^. 1 1 0.000000 10.000000 0.000000 l/liiiUli; 60 1 6.463726 501717 000000 00 6.463726 501717 13.536274 59 2 764756 293485 000000 00 764756 293483 235244 58 3 940847 208231 000000 00 940847 208231 059153 57 4 7.065786 161517 000000 00 7.065786 161517 12.934214 56 5 162696 131968 000000 00 162696 131969 837304 55 6 241877 111575 9.999999 01 241878 111578 758122 54 7 308824 96653 999999 01 308825 99653 691175 53 8 366816 85254 999999 01 366817 85254 633183 52 9 417968 76263 999999 01 417970 76263 582030 51 10 11 463725 68988 999998 01 01 463727 68988 538273 50 49 7.505118 62981 9.999998 7.505120 62981 12.494880 12 542906 57936 999997 01 542909 57933 457091 48 13 577668 53841 999997 01 577673 53642 422328 47 14 609853 49938 999996 01 609857 49939 390143 46 15 639816 46714 999996 01 639820 46715 360180 45 16 667845 43881 999995 01 667849 43882 332151 44 17 694173 41372 999995 01 6941 78 41373 305821 43 18 718997 39135 999994 01 719003 39136 280997 42 19 742477 37127 999993 01 742484 37128 257516 41 20 21 764754 7.785943 35315 999993 9.999992 01 01 764761 35136 235239 40 39 33672 7.785951 33673 12.214049 23 806146 32175 999991 01 806155 32176 193845 38 23 825451 30805 999990 01 825460 30806 174540 37 24 843934 29547 999989 02 843944 29549 156056 36 25 861662 28388 999988 02 861674 28390 138326 35 26 878695 27317 999988 02 878708 27318 121292 34 27 895085 26323 999987 02 895099 26325 104901 33 28 910879 25399 999986 02 910894 25401 089106 32 29 926119 24538 999985 02 926134 24540 073866 31 30 31 940842 23733 999983 02 02 940858 23735 059142 30 29 7.955082 22980 9.999982 7.955100 22981 13.044900 32 968870 22273 999981 02 968889 22275 031111 28 33 982233 21608 999980 02 982253 21610 017747 27 34 995198 20981 999979 02 995219 20983 004781 26 35 8.007787 20390 999977 02 8.007809 20392 11.992191 25 36 020021 19831 999976 02 020045 18883 979955 34 37 031919 19302 999975 02 031945 19305 968055 33 38 043501 18801 999973 03 043527 18803 956473 32 39 054781 18325 999972 02 054809 18327 945191 21 40 41 065776 17873 17441 999971 02 03 065806 8.076531 17874 17444 934194 20 19 8.076500 9.999969 11.923469 42 086965 17031 999968 02 086997 17034 913003 18 43 097183 16639 999966 02 097317 16642 902783 17 44 107167 16265 999964 03 107202 16238 892797 16 45 116926 15908 999963 03 118963 15910 883037 15 46 126471 15566 999961 03 126510 15568 873490 14 47 135810 15238 999959 03 135851 15241 864149 13 48 144953 14924 999958 03 144996 14:J27 855004 13 49 153907 14622 999956 03 153953 14627 846048 11 50 51* 162681 8.171280 14333 14054 999954 03 03 163727 14336 837273 10 9 9.9y9952 8.171328 14057 11.828672 52 179713 137S6 999950 03 179763 13790 830237 8 53 187985 13529 999948 03 188036 13532 811964 7 54 196102 13280 999946 03 196156 13284 80384^1 6 55 204070 13041 999944 3 204126 13044 795874 5 56 211895 12810 999942 4 211953 13814 788047 4 57 219581 12587 999940 04 219641 12590 780359 3 58 227134 12372 999938 04 227195 13376 772805 2 59 234557 12164 999936 04 234621 12168 765379 1 60 241855 11963 999934 04 241931 11967 758079 ~ Cosine j Sine 1 Colang. Tang. 1 M. | 8'J De-reos. SINES A^■D TANGENTS. (1 Degiec.) 19 M. Sine D. 1 Cosine | D. Tang. D. Cotang. 1 "1 "T 8.241855 11963 9.999934 04 8.241921 11967 11.758079 60 1 249033 11768 999932 04 249102 11772 ■ 750898 59 2 256094 11580 999929 04 258165 11584 743835 58 3 263042 11398 999927 04 263115 11402 736885 57 4 269881 11221 999925 04 269956 11225 730044 56 5 276614 11050 999922 04 276691 11054 723309 55 6 283243 10883 999920 04 283323 10887 716677 54 7 289773 10721 999918 04 289856 10726 710144 53 8 296207 10565 999915 04 296292 10570 703708 52 9 302546 10413 999913 04 302634 10418 697366 51 10 11 308794 8.314954 10266 999910 9.999907 04 04 308884 8.315046 10270 10126 691116 50 49 10122 11.684954 12 321027 9982 999905 04 321122 9987 678878 AS 13 327016 9847 999902 04 327114 9851 672886 47 14 332924 9714 999899 05 333025 9719 686975 46 15 333753 9586 999897 05 338S56 9590 661144 45 16 344504 9460 999894 05 344610 9465 655390 44 17 350181 9338 999S91 05 350289 9343 649711 43 18 355783 9219 999888 05 355895 9224 644105 42 19 361315 9103 999885 05 361430 9108 638570 41 20 21 366777 8990 999882 9.999879 05 05 366895 8995 633105 40 39 8.372171 8880 8.372292 8885 11.627708 22 377499 8772 999876 05 377622 8777 622378 38 23 382762 8637 999873 05 382889 8672 617111 37 24 387962 8564 999870 05 388092 8570 611908 36 25 393101 8464 999867 05 393234 8470 606766 35 26 398179 8366 999864 05 398315 8371 601685 34 27 403199 8271 999861 05 403338 8276 596662 33 28 408161 8177 999858 05 408304 8182 591696 32 29 413068 8086 999854 05 413213 8091 586787 31 30 31 417919 7996 999851 06 06 418068 8002 581932 30 29 8.422717 7909 9.999848 8.422869 7914 11.577131 32 427462 7823 999844 06 427618 7830 572382 28 33 432156 7740 999841 06 432315 7745 567685 27 34 436800 7657 999838 06 436962 7663 563038 26 35 441394 7577 999S34 06 441560 7583 558440 25 36 445941 7499 999831 06 446110 7505 553890 24 37 450440 7422 999827 06 450613 7428 549387 23 38 454893 7346 999823 06 455070 7352 544930 22 39 459301 7273 999820 06 459481 7279 540519 21 40 41 463665 7200 999816 9.999812 06 06 463849 7206 536151 11.531828 20 19 8.467985 7129 8.468172 7135 42 472263 7060 999809 08 472454 7066 527546 18 43 476498 6991 999805 08 476693 6998 523307 17 44 480693 6924 999801 06 480892 6931 519108 16 45 4848-18 6859 999797 07 485ft50 6865 514950 15 46 488963 6794 999793 07 489170 6801 510830 14 47 493040 6731 999790 07 493250 6738 506750 13 48 497078 6669 999786 07 497293 6676 502707 12 49 501080 6608 999782 07 .501298 0615 498702 11 50 51 505045 6548 999778 07 07 505267 8.509200 6555 494733 10 9 8.508974 6489 9.999774 6496 11.490800 52 512867 6431 999769 07 513098 6439 486902 8 53 516726 6375 999765 07 516961 6382 483039 7 54 520551 6319 999761 07 520790 6326 479210 6 55 524343 6264 999757 07 524586 6272 475414 5 56 528102 6211 999753 07 528349 6218 471651 4 57 531828 6158 999748 07 532080 6165 467920 3 58 535523 6106 . 999744 07 535779 6113 464221 2 59 539180 6055 999740 07 5394i7 6062 460553 1 60 542819 6004 999735 07 54303/1 6012 45691G -i Cosine Sine 1 Cotung. Tuns- 1 m. j US Degrees. 20 (2 Degrees.) a TABLE OF LOGARITHMIC 11 i Sine ». Closine | D. Tang. 1 D. 1 rotan?. 1 1 T 8.542819 6004 9.999735 07 8.543084 6012 11.456916 60 1 546422 5955 999731 07 546691 5962 453309 59 2 549995 5906 999726 07 .550268 5914 449732 58 3 553539 5858 999722 08 553817 5866 446183 57 4 557054 5811 999717 08 557336 5819 442664 56 5 560540 5765 999713 08 560828 5773 439172 55 6 563999 5719 999708 08 564291 5727 435709 54 7 567431 5674 999704 08 567727 5682 432273 53 8 570836 5630 999699 08 571137 5638 428863 52 9 574214 5587 999694 08 574520 5595 425480 51 10 11 577566 8.580892 5544 999689 08 OS 577877 5552 422123 50 49 5502 9.999685 8.581208 6510 11.418792 12 584193 5460 999680 08 584514 5468 415486 48 13 587469 5419 999675 08 587795 5427 412205 47 14 590721 5379 999670 08 591051 5387 408949 46 15 593948 5339 999665 08 694283 6347 405717 45 16 597152 5300 999660 08 597492 5308 402508 44 17 600332 5261 999655 08 600677 5270 399323 43 18 603489 5223 999650 08 603839 5232 396161 42 19 606323 5186 999645 09 606978 5194 393022 41 20 21 609734 8.612823 5149 999640 9.999035 09 09 610094 8.613189 5158 389906 40 39 5112 5131 11.386811 22 615891 5076 999629 09 616262 5085 383738 38 23 618937 5041 999624 09 619313 5050 380687 37 24 621962 5006 999619 09 622343 5015 377657 36 25 624965 4972 999614 09 625352 4981 374648 35 26 627948 4938 999608 09 628340 4947 371660 34 27 630911 4904 999603 09 631308 4913 368692 33 28 633854 4871 999597 09 634256 4880 365744 32 29 636776 4839 999592 09 637184 4848 362816 31 30 31 639680 8.642563 4803 999586 9.999581 09 09 640093 4816 359907 30 29 4775 8.642982 4784 11.357018 32 645428 4743 999575 09 645853 4753 354*147 28 33 648274 4712 999570 09 648704 4722 351296 27 34 651102 4682 999564 09 651537 4691 348463 26 35 653911 4652 999558 10 654352 4661 345648 25 36 656702 4622 999553 10 657149 4631 342851 24 37 659475 4592 999547 10 659928 4602 340072 23 38 662230 4563 999541 10 662689 4573 337311 22 39 664968 4535 999535 10 665433 4544 334567 21 40 41 667689 8.670393 4506 4479 999529 10 10 688160 4526 331840 20 19 9.999524 8.670870 4488 11.329130 42 673080 4451 999518 10 673663 4461 326437 18 43 675751 4424 999512 10 676239 4434 323761 17 44 678405 4397 999506 10 678900 4417 321100 16 45 681043 4370 999500 10 681544 4380 318456 15 46 683665 4344 999493 10 684172 4354 315828 14 47 686272 4318 999487 10 686784 4328 313216 13 48 688863 4292 999481 10 689381 4303 310619 12 49 691438 4267 999476 10 691963 4277 308037 11 50 51 693998 8.696543 4242 999469 9.999463 10 11 694529 8.697081 4252 305471 10 9 4217 4228 11.302919 52 699073 4192 999456 11 699617 4203 300383 8 53 701589 4168 999450 11 702139 4179 297861 7 54 704090 4144 999443 11 704646 4155 295354 6 55 706577 4121 999437 11 707140 4132 292860 5 56 709049 4097 999431 11 709618 4108 290382 4 57 711507 4074 999424 11 712083 4085 287917 3 58 713952 4051 999418 11 714534 4062 285465 2 59 716383 4029 999411 11 716972 4040 283028 1 60 718800 4006 999404 11 719396 4017 280604 01 , Cosine 1 Sme 1 Cotang. 1 1 Tang. |M. 1 87 Degrees. SINES AND TANGENTS. (3 Degrees.) 21 ' nn Siae 1 D. i Cosine 1 D | Cansr 1 i. 1 ro-Hiu'. 1 1 8.718800 4006 1 9.999404 11 8.719396 4017 11.280604 "60" 1 721204 3984 999398 11 721806 3995 278194 59 2 723595 3962 999391 11 724204 3974 275796 58 3 725972 3941 999384 11 726588 3952 273412 57 4 728337 3919 999378 11 728959 3930 271041 56 5 730688 3898 999371 11 731317 3909 268683 55 6 733027 3877 999364 12 733663 3889 266337 54 7 735354 3857 999357 12 735996 3868 264004 53 s 737667 3836 999350 12 738317 3848 261683 ,52 9 739969 3816 999343 12 740626 3827 259374 51 10 11 742259 8.744536 3796 999336 9.999329 12 12 742922 3807 257078 50 49 3776 8.745207 3787 11.254793 12 746802 3756 999322 12 747479 3768 252521 48 13 749055 3737 999315 12 749740 3749 250260 47 14 751297 3717 999308 12 751989 3729 248011 46 15 753528 3698 999301 12 754227 3710 245773 45 16 755747 3679 999294 12 756453 3692 243547 44 17 757955 3661 999286 12 758668 3673 241332 43 18 760151 3642 999279 12 760872 3655 239128 42 19 762337 3624 999272 12 763065 3636 236935 41 20 21 764511 3606 999265 9.999257 12 12 765246 3618 234754 40 39 8.766675 3588 8.767417 3600 11.232583 22 768828 3570 999250 13 769578 3583 230422 38 23 770970 3553 999242 13 771727 3565 228273 37 24 773101 3535 999235 13 773866 3548 226134 36 25 775223 3518 999227 13 775995 3531 224005 35 26 777333 3501 999220 13 778114 3514 221886 34 27 779434 3484 999212 13 780222 3497 219778 33 28 781524 3467 999205 13 782320 3480 217680 32 29 783605 3451 999197 13 784408 3464 215592 31 30 31 785675 3431 999189 9.999181 13 13 786486 8.788554 3447 3431 213514 30 29 8.787736 3418 11.211446 32 789787 3402 999174 13 790613 3414 209387 28 33 791828 3386 999166 13 792662 3399 207338 27 34 793859 3370 999158 13 794701 3383 205299 26 35 795881 3354 999150 13 796731 3368 203269 25 36 797894 3339 999142 13 798752 3352 201248 24 37 799897 3323 999134 13 800763 3337 199237 23 38 801892 3308 999126 13 802765 3322 197235 22 39 803876 3293 999118 13 804758 3307 195242 21 40 41 805852 8.807819 3278 999110 9.999102 13 13 806742 8.808717 3292 193258 20 19 3263 3278 11.191283 42 809777 3249 999094 14 810683 3262 189317 18 43 811726 3234 999086 14 812641 3248 187359 17 44 813667 3219 999077 14 814589 3233 185411 16 45 815599 3205 999069 14 816529 3219 183471 15 46 817522 3191 999061 14 818461 3205 181539 14 47 819436 3177 999053 14 820384 3191 179616 13 48 821343 3163 999044 14 822298 3177 177702 12 49 823240 3149 999036 14 824205 3163 175795 11 50 51 825130 8.827011 3135 999027 9.999019 14 14 82^03 3150 173897 10 9 3122 8.827992 3136 11.172008 52 828884 3108 999010 14 829874 3123 170126 8 53 830749 3095 999002 14 831748 3110 168252 7 54 832607 3082 998993 14 8.33613 3096 166387 6 55 834456 3069 998984 14 835471 3083 164529 5 56 836297 3056 998976 14 837321 3070 162679 4 57 838130 3043 998967 15 839163 3057 160837 3 58 839956 3030 998958 15 840998 3045 159002 2 59 841774 3017 998950 15 842825 3032 157175 1 60 843585 3000 998941 15 844644 3019 155356 ~ Cosine 1 1 «*■- 1 1 Cotang. 1 Tang. j M. | 86 Degrees. (4 Degrees.) a table of logarithmic M.| Sine D. 1 Cosine 1 D. | Tan?. 1 D- 1 Cotang. 1 ] 8.843585 3005 9.998941 15 8.844644 3019 11.155356 60 1 845387 2992 998932 15 846455 3007 153545 59 2 847183 2980 998923 15 848260 2995 151740 58 3 848971 2967 998914 15 850057 2982 149943 57 4 850751 2955 998905 15 851846 2970 148154 56 5 852525 ^943 998896 15 853628 2958 146372 55 6 854291 2931 998887 16 855403 2946 144597 54 7 856049 2919 998878 15 857171 2935 142829 53 8 857801 2907 998869 15 858932 2923 141068 52 9 85954(5 2896 998860 15 860686 2911 139314 51 10 11 861283 2884 " 2873 998851 15 15 862433 2900 2888 137567 11.135827 50 49 8.863014 9.998841 8.864173 12 864738 2861 998832 15 865906 2877 134094 48 13 866455 2850 Q98823 16 867632 2868 132368 47 14 868165 2839 998813 16 869351 2854 130649 46 15 869868 2828 998804 16 871064 2843 128936 45 16 871565 2817 99S795 16 872770 2832 127230 44 17 873255 2806 998785 16 874469 2821 125531 43 18 874938 2795 998776 16 876162 2811 123838 42 19 876615 2786 998766 16 877849 2800 122151 41 20 21 878285 2773 998757 9.998747 16 16 879529 2789 120471 40 39 8.879949 2763 8.881202 2779 11.118798 22 881607 2752 998738 16 882869 2768 117131 38 23 883258 2742 998728 16 884530 2758 115470 37 24 884903 2731 998718 16 886185 2747 113815" 36 25 886542 2721 998708 16 887833 2737 112167 35 26 888174 2711 998699 16 889476 2727 110524 34 27 889801 2700 998689 16 891112 2717 108888 33 28 891421 2690 998679 16 892742 2707 107258 32 29 893035 2680 998669 17 894366 2697 105634 31 30 31 894643 8.896246 2670 S98659 9.998649 17 17 895984 2687 104016 30 29 2660 8.897596 2677 11.102404 32 897842 2651 998639 17 899203 2667 100797 28 33 899432 2641 998629 17 900803 2658 099197 27 34 901017 2631 998619 17 902398 2648 097602 26 35 902596 2622 998609 17 903987 2638 096013 25 36 904169 2612 998599 17 905570 2629 094430 24 37 905736 2603 998589 17 907147 2620 092853 23 38 907297 2593 998578 17 908719 2610 091281 22 39 908853 2584 998568 17 910285 2601 039715 21 40 41 910404 2575 2566 998558 17 17 911846 2592 088154 20 19 8.911949 9.998548 8.913401 2583 11.086599 42 913488 2556 998537 17 914951 2574 085049 18 43 915022 2547 998527 17 916495 2585 083505 17 44 916550 2538 998516 18 918034 2556 ■ 081966 16 45 918073 2529 998506 18 919568 2547 080432 15 46 919591 2520 998495 18 921096 2538 078904 14 47 921103 2512 998485 18 922619 2530 077381 13 48 922610 2503 998474 18 924136 2521 075864 12 49 924112 2494 998464 18 925649 2512 074351 11 50 51 925609 2486 9^453 18 18 927156 2503 072844 10 9 8.927100 2477 9.998442 8.928658 2495 11.071342 52 928587 2469 998431 18 930155 2486 069845 8 53 930068 2460 998421 18 931647 2478 068353 7 54 931544 2452 998410 18 933134 2470 066866 6 55 933015 2443 998399 18 934616 2461 065384 5 56 934481 2435 998388 18 936093 2453 063907 4 57 935942 2427 998377 18 937565 2445 062435 3 58 937398 2419 998366 18 939032 2437 060968 2 59 938850 2411 998355 18 940494 2430 059506 1 60 940296 2403 998344 18 941952 2421 058048 C Cosine 1 1 Sine j 1 Cotang. j Tang. Twr 85 Degrees. SINES AND TANGENTS. (5 DegTeCS. ) 23 T Sine 1 D. Cosiii« 1 D. •rv.„!f. 1 D. CoMU's:. 1 1 8.940296 24i>3 9 . 998344 19 8.941952 2421 11.058048 60 1 941738 2394 998333 19 943404 2413 056596 59 2 943174 2387 998322 19 944852 2405 055148 58 3 941606 2379 998311 19 946295 2397 053705 57 4 946034 2371 998300 19 947734 2390 052266 56 5 947456 2363 998239 19 949168 2382 050832 55 6 948874 2355 998277 19 950597 2374 049403 54 7 950287 2348 998236 19 952021 2366 047979 53 8 951696 2340 998255 19 953441 2360 046559 52 9 953100 2332 998243 19 954856 2351 045144 51 10 11 954499 8.955894 2325 998232 9.998220 19 19 956267 2344 043733 50 49 2317 8.957674 2337 11.042326 12 957284 2310 998209 19 959075 2329 040925 48 13 958670 2302 998197 19 960473 2323 039527 47 14 960052 2295 998186 19 961866 2314 038134 46 15 961429 2288 99S174 19 963255 2307 036745 45 16 962801 2280 998163 19 964639 2300 035361 44 17 964170 2273 998151 19 968019 2293 033981 43 18 965534 2266 998139 20 967394 2286 032606 42 19 966893 2259 998128 20 968766 2279 031234 41 20 21 968249 8.969600 2252 998116 9.998104 20 20 970133 8.971496 2271 029867 40 39 2244 2265 11.028504 32 970947 2238 998092 20 972855 2257 027145 38 23 972289 2231 998080 20 974209 2251 025791 37 24 973628 2224 998068 20 975560 2244 024440 36 25 974962 2217 998056 20 976906 2237 023094 35 26 976293 2210 99S044 20 978248 2230 021752 34 27 977619 2203 998032 20 979586 2223 020414 33 28 978941 2197 998020 20 980921 2217 019079 32 29 980259 2190 998008 20 982251 2210 017749 31 30 31 98 1573 8.982S83 2183 997996 20 20 983577 8.984899 2204 016423 30 29 2177 9.997984 2197 11.015101 32 984189 2170 997972 20 986217 2191 013783 28 33 985491 2163 997959 20 987532 2184 012468 27 34 986789 2157 997947 20 988842 2178 011158 26 35 988083 2150 997935 21 990149 2171 009851 25 36 989374 2144 997922 21 991451 2165 008549 24 37 990660 2138 997910 21 992750 2158 007250 23 38 991943 2131 997897 21 994045 2152 005955 22 39 993222 2125 997885 21 995337 2146 004663 21 40 41 994497 8.995768 2119 997872 9.997860 21 21 996624 8.997908 2140 003376 20 19 2112 2134 11.002092 42 997036 2106 997847 21 999188 2127 000812 18 43 998299 2100 997835 21 9.000465 2121 10.999535 17 44 999560 2094 997822 21 001738 2115 998262 16 45 9.000816 2087 997809 21 003007 2109 996993 15 46 002069 2082 997797 21 004272 2103 995728 14 47 003318 2076 997784 21 005534 2097 994466 13 48 004563 2070 997771 21 006792 2091 993208 12 49 005805 2064 997758 21 008047 2085 991953 11 50 51 007044 9.008278 2058 997745 9.997732 21 21 009298 9.010546 2080 990702 9 2052 2074 10.989454 52 009510 2046 997719 21 011790 2068 988210 8 53 010737 2040 997706 21 013031 2062 986969 7 54 011962 2034 997693 22 014268 2056 985732 6 55 013182 2029 997680 22 015502 2051 984498 5 56 014400 2023 997667 22 016732 2045 983268 4 57 015613 2017 997654 22 017^59 2040 982041 3 58 016824 2012 997641 22 019183 2033 980817 2 59 018031 2006 997628 22 020403 2028 979597 1 60 019235 2000 997614 22 021620 2023 978380 „^_ C isine | | Sine 1 ] Cotang. Tang. |M. 1 84 Degrees. M (6 Degrees.) a TABLE OF LOGAEITHMIC M. s-.^ D. ! ( ..Mi-.e i D. Tang. 1 D. 1 Cotaiig. j 1 ~T 9.019235 2000 9.997614 22 9.021620 2023 10.978380 60 1 020435 1995 997601 22 022834 2017 977166 59 2 021632 1989 997588 22 024044 2011 975956 58 3 022825 1984 997574 22 025251 2006 974749 57 4 024016 1978 997561 22 026455 2000 973545 56 5 025203 1973 997547 22 027655 1995 972345 55 6 026386 1967 997534 23 028S52 1990 971148 54 7 027567 1962 997520 23 030046 1985 969954 53 8 028744 1957 997507 23 031237 1979 968763 52 9 029918 1951 097493 23 032425 1974 967575 51 10 031089 1947 997480 23 033609 1969 966391 50 U 9.032257 1941 9.997466 23 9.034791 1964 10.965209 49 12 033421 1936 997452 23 035969 1958 964031 48 13 0345S2 1930 997439 23 037144 1953 962856 47 14 035741 1925 997425 23 038316 1948 961684 46 15 036896 1920 997411 23 039485 1943 960515 45 16 038048 1915 997397 23 040651 1938 959349 44 17 039197 1910 997383 23 041813 1933 9.58187 43 18 040342 1905 997369 23 042973 1928 957027 42 19 041485 1899 997355 23 044130 1923 955870 41 20 21 042625 1894 1889 997341 9.997327 23 24 045284 9.046434 1918 954716 40 39 9.043762 1913 10.953566 22 044895 1884 997313 24 047582 1908 9.52418 38 23 046026 1879 997299 24 048727 1903 951273 37 24 047154 1875 997285 24 049869 1898 950131 36 25 048279 1870 997271 24 051008 1893 943992 35 26 049400 1865 997257 24 052144 1889 947856 34 27 050519 1860 997242 24 053277 1884 946723 33 28 051635 1855 997228 24 054407 1879 945593 32 29 052749 1850 997214 24 055535 1874 944465 31 30 31 053859 054966 1845 1841 997199 24 24 056659 9.057781 1870 943341 30 29 9.997185 1865 10.942219 32 056071 1836 997170 24 058900 1869 941100 28 33 057172 1831 997156 24 060016 1855 939984 27 34 058271 1827 997141 24 061130 1851 93SS70 26 35 059367 1822 997127 24 062240 1846 937760 25 36 060460 1817 997112 24 06334-8 1842 936652 24 37 081551 1813 99709S 24 064453 1837 935547 23 38 062639 1803 997083 25 065556 1833 934444 22 39 063724 1804 997068 25 066655 1828 933345 21 40 41 064S06 1799 1794 997053 25 25 067752 9.068846 1824 1819 932248 20 19 9.0658S5 9.997039 10.931154 42 066962 1790 997024 25 069938 1815 930062 18 43 068036 1786 997009 25 071027 1810 928973 17 44 069107 1781 996994 25 072113 1806 927887 16 45 070176 1777 996979 25 073197 1802 926803 15 46 071242 1772 996964 25 074278 1797 925722 14 47 072306 1768 996949 25 075356 1793 924644 13 48 073366 1763 996934 25 076432 1789 923568 12 49 074424 1759 996919 25 077505 1784 922495 11 50 51 075480 9.076533 1755 1750 996904 25 25 078576 9.079644 1780 1776 921424 10 9 9.996889 10.920356 52 077583 1746 996874 25 080710 1772 919290 8 ,53 078631 1742 996858 ,25 081773 1767 918227 7 64 079676 1738 996843 ',25 082S83 1763 917167 6 55 080719 1733 996828 25 083S91 1759 916109 5 56 081759 1729 996812 ;26 084947 1755 915053 4 57 082797 1725 996797 '26 086000 1751 914000 3 58 0S3S32 1721 996782 26 087050 1747 912950 2 59 0S4S64 085894 1717 996766 ,26 08S09S 1743 911902 1 60 1713 996751 |26 089144 i 1738 910856 Cosine Sine 1 1 Civam. 1 Tang. |M.| i3 Degrees. SI^-ES AND TANGENTS. (7 Degrees.) 25 _Mj_ Sine I D. I Cosine | D. | Tang. 1 D. | Cotang. 1 1 9.085894 1713 9.9967511 26] 9.089144 1738 j LO. 910856 60 1 086922 1709 996735! 26 090187 1734 | 909813 59 2 087947 1704 996720! 26 091228 1730 908772 58 3 088970 1700 9967041 26 092266 1727 907734 57 4 089990 1696 996688 26 093302 1722 906698 56 5 091008 1692 996673 26 094336 1719 905664 55 6 092024 1688 996657 26 095367 1715 904633! 54 7 093037 1684 996641 26 096395 1711 903605 53 8 094047 1680 996625 26 097422 1707 902578 52 9 095056 1676 996610 26 098446 1703 901554 51 10 096062 1673 996594 26 099468 1699 900532 50 11 9.097065 1668 9.996578 27 9.100487 1695 10.899513 49 12 098066 1665 996562 27 101504 1691 898496 48 13 099065 1661 996546 27 102519 1687 897481 47 14 100062 1657 996530 27 103532 1684 896468 46 15 101056 ^1653 996514 27 104542 1680 895458 45 16 102048 1649 996498 27 105550 1676 894450 44 17 103037 1645 996482 27 106556 1672 893444 43 18 104025 1641 996465 27 107559 1669 892441 42 19 105010 1638 996449 27 108560 1665 891440 41 20 21 105992 1634 996433 27 27 109559 1661 890441 40 39 9.106973 1630 9.996417 9.110556 1658 10.889444 22 107951 1627 996400 27 111551 1654 888449 38 23 108927 1623 996384 27 112543 1650 887457 37 24 109901 1619 996368 27 113533 1646 886467 36 25 110873 1616 996351 27 114521 1643 885479 35 26 111842 1612 996335 27 115507 1639 884493 34 27 112809 1608 996318 27 116491 1636 883509 33 28 X13774 1605 996302 28 117472 1632 882528 32 29 114737 1601 996285 28 118452 1629 881548 31 30 31 115698 1597 996269 9.996252 28 28 119429 1625 880571 30 29 9.11^656 1594 9.120404 1622 10.879596 32 117613 1590 996235 28 121377 1618 878623 28 33 118567 1587 996219 28 122348 1615 877652 27 34 119519 1583 996202 28 123317 1611 876683 26 35 120469 1580 996185 28 124284 1607 875716 25 36 121417 1576 996168 28 125249 1604 874751 24 37 122362 1573 996151 28 126211 1601 873789 23 38 123306 1569 996134 28 127172 1597 872828 22 39 124248 1566 996117 28 128130 1594 871870 21 40 41 125187 1562 996100 28 29 129087 1591 870913 20 9.126125 1559 9.996083 9.130041 1587 10.869959 19 42 127060 1556 996066 29 130994 1584 869006 18 43 127993 1552 996049 29 131944 1581 868056 17 44 128925 1549 996032 29 132893 1577 867107 16 45 129854 1545 996015 29 133839 1574 866161 15 46 130781 1542 995998 29 134784 1571 865216 14 47 131706 1539 995980 29 135726 1567 864274 13 48 132630 1535 995963 29 136667 1564 863333 12 49 133551 1532 995946 29 137605 1561 862395 11 50 51 134470 9.135387 1529 995928 29 29 138542 1558 1555 861458 10 1525 9.995911 9.139476 10.860524 9 52 136303 1522 995894 29 140409 1551 859591 8 53 137216 1519 995876 29 141340 1548 858660 7 54 138128 1516 995859 29 142269 1545 857731 6 55 139037 1512 995841 29 143196 1542 856804 5 56 139944 1509 995823 29 144121 1539 855879 4 57 14085(] 1506 995806 29 145044 1535 854956 3 58 141754 t 1503 995788 29 145966 1532 854034 2 59 14265J 1500 995771 29 146885 1529 853115 1 60 14355£ 1 1496 995753 29 147803 1 1526 852197 = 1 Cosine 1 1 Sine 1 1 r,',,n.. J 1 Tang. 1 M! 82 Deg rees. 26 ( 8 Degrees.) a TAJ3LE OF LOGARITHMIC 1 Sine 1 D. 1 Cosrne | D, 1 Ta;lg. 1 I). 1 C^taii^. j 1 9.14355. 5 1496 9.995753 30 j 9.147803 1526 10.852197; 60 1 14445J J 1493 995735 30 I 148718 1523 851282 59 2 14534{ ) 1490 995717 30 i 149632 1620 850368 58 3 14624C J 1487 995699 30 I 150544 1517 849456; 57 4 14713( 5 1484 995681 30 ' 151454 1514 1 848546! 56 5 148026 5 1481 995664 30 ! 152363 1511 847637; 55 6 14891c ) 1478 995646 30 153269 1508 846731154 7 14980S 1475 995628 30 154174 1505 845826 53 8 150686 1472 995610 30 155077 1502 844923' 52 9 ! 15156S 1469 995591 30 155978 1499 844022; 21 10 11 152451 9 153330 1466 1 1463 995573 ,' 9.995555 30 30 I 156877 i 9.157775 1496 843123 50 1493 10.842225149 12 154208 1 1460 ' 995537 30 158671 1490 841329 48 13 155083 i 1457 995519 30 159565 1487 840435 47 14 155957 1454 995501 31 160457 1484 8395431 46 15 156830 1451 995482 31 161347 1481 838653 45 16 157700 1448 995464 31 163236 1479 837764 44 17 158569 1445 995446 31 163123 1476 836877 43 18 159435 1442 995427 31 164008 1473 835992 42 19 1G0301 1439 995409 31 164892 1470 8351081 41 I 20 21 161164 9.162025 1436 1433 995390 31 31 165774 9.166654 1467 834226 40 9.995372 1464 10.833346 39 22 162885 1430 995353 31 167532 1461 832468J 38 23 163743 1427 995334 31 168409 1458 83159l| 37 24 164600 1424 995316 31 169284 1455 8307161 36 25 165454 1422 995297 31 170157 14.53 6298431 35 26 166307 1419 995278 31 171029 1450 828971 34 27 167159 1416 995260 31 171899 1447 828101 33 28 168008 1413 995241 32 172767 1444 827233 32 29 168856 1410 995222 32 173634 1442 826366 31 30 31 169702 9.170547 1407 995203 32 32 174499 1439 1436 825501 30 29 1405 9.995184 9.175362 10.824638 32 171389 1402 995165 32 176224 1433 823776 28 33 172230 1399 995146; 32 177084 1431 822916 27 34 173070 1396 995127! 32 177942 1428 822058; 26 35 173908 1394 995108! 32 178799 1425 8212011 25 36 174744 1391 995089; 32 179655 1423 820345; 24 37 175578 1388 995070 32 180508 1420 8194921 23 38 176411 1386 995051 32 181360 1417 818640 22 39 177242 1383 995032 32 182211 1415 817789 21 40 41 178072 1380 995013 9.994993 32 32 183059 1412 816941 20 19 9.178900 1377 9.183907 1409 10.816093 42 179726 1374 994974 32 184752 1407 815248 18 43 180551 1372 9949551 32 185597 1404 8144^3 17 44 181374 1369 994935! 32 186439 1402 813561 16 45 182196 1366 994916! 33 187280 1399 8127201 15 46 183016 1364 9948961 33 188120 1396 811880 14 47 183834 1361 994877 33 188958 1393 811042 13 48 184651 1359 9948571 33 189794 1391 810206; 12 49 185466 1356 9948381 33 190629 1389 809371! 11 50 51 186280 1353 9948181 9.994798! 33 33 191462 9.192294 13S6 1384 808538 10 9.187092 1351 1 10.807706 9 52 187903 1348 9947791 33 193124 1381 8068761 8 53 188712 1346 994759; 33 193953 1379 806047] 7 54 189519 1343 994739 33 194780 1376 8052201 6 55 190325 1341 994719 33 195606 1374 S04394J 5 56 191130 1338 i 994700i 33 196430 1371 803570! 4 57 191933 1336 ' 9946801 33 197253 1369 8027471 3 58 192734 1.333 j 994660' 33 198074 1366 8019261 2 69 193534 1330 994640 1 33 198894 1364 801106 1 60 194332 1328 994620; 33 1 199713 1361 8002871 ^ Cosine ] i .>^me 1 1 Cotaus. 1 I Tang. 1 M. 81 DeffJiics. SINES AND TAIN'GENTS . (9 De grees.j 27 nrr Sine 1 D. 1 Cosiue i D. 1 Tang. 1 D- I Cotang. 1 1 9.194332 1328 9.994620 33 9.199713 1361 10.800287 60 1 195139 1326 994600 33 200529 1359 799471 59 2 195925 1323 994580 33 201345 1356 798655 68 3 196719 1321 994560 34 202159 1354 797841 57 4 197511 1318 994540 34 202971 1352 797029 56 5 198302 1316 994519 34 203782 1349 796218 55 6 199091 1313 994499 34 204592 1347 795408 54 7 199879 1311 994479 34 205400 1345 794600 53 8 200666 1308 994459 34 206207 1342 793793 52 9 201451 1306 994438 34 207013 1340 792987 51 10 11 202234 1304 1301 994418 34 34 207817 1338 792183 10.791381 50 49 9.203017 9.994397 9.208619 1335 12 203797 1299 994377 34 209420 1333 790580 48 13 204577 1296 994357 34 210220 1331 789780 47 14 205354 1294 994336 34 211018 1328 788982 46 15 206131 1292 994316 34 211815 1326 788185 45 16 206906 1289 994295 84 212611 1324 787389 44 17 207679 1287 994274 35 213405 1521 786595 43 18 208452 1285 994254 35 214198 1319 785802 42 19 209222 1282 994233 35 214989 1317 '?85011 41 20 21 209992 9.210760 1280 994212 35 35 215780 9.216568 1315 784220 40 39 1278 9.994191 1312 10.783432 22 211526 1275 994171 35 217356 1310 782644 38 23 212291 1273 994150 35 218142 1308 781858 37 24 213055 1271 994129 35 218926 1305 781074 36 25 213818 1268 994108 35 219710 1303 780290 35 26 214579 1266 994087 35 220492 1301 779508 34 27 215338 1264 994066 35 221272 1299 778728 33 28 216097 1261 994045 35 222052 1297 777948 32 29 216854 1259 994024 35 222830 1294 777170 31 30 31 217609 1257 994003 35 35 223606 1292 776394 30 29 9.218363 1255 9.993981 9.224382 1290 10.775618 32 219116 1253 993960 35 225156 1288 774844 28 33 219868 1250 993939 35 225929 1286 774071 27 34 220618 1248 993918 35 226700 1284 773300 26 35 221867 1246 993896 36 227471 1881 772529 25 36 222115 1244 993875 36 228239 1279 771761 24 37 222861 1242 993854 36 229007 1277 770993 23 38 223606 1239 993832 36 229773 1275 770227 22 39 224349 1237 993811 36 230539 1273 769461 21 40 41 225092 1235 993789 9.993768 36 36 231302 1271 768698 20 19 9.225833 1233 9.232065 1269 10.767935 42 226573 1231 993746 36 232826 1267 767174 18 43 227311 1228 993725 36 233586 1265 766414 17 44 228048 1226 993703 36 234345 1262 765655 16 45 228784 1224 993681 36 235103 1260 '/.64897 15 46 229518 1222 993660 36 235869 1258 764141 14 47 230252 1220 993638 36 236614 1256 763386 13 48 230984 1218 993616 36 237368 1254 762632 12 49 231714 1216 993594 37 238120 1252 761880 11 50 51 232444 9.233172 1214 993572 37 37 238872 9.239622 1250 761128 10 9 1212 9.993550 1248 10.7603.78 52 2.33899 1209 993528 37 240371 1246 759629 8 53 234625 1207 993506 37 241118 1244 758882 7 54 235349 1205 993484 37 241865 1242 758135 6 55 236073 1203 993462 37 242610 1240 757390 5 56 236795 1201 993440 37 243354 1238 756646 4 57 237515 1199 993418 37 244097 1236 755903 3 58 238235 1197 993396 37 244839 1234 7.55161 2 59 238953 1195 993374 37 245579 1232 754421 1 60 239670 1193 993351 37 246319 1230 753681 Cosine 1 1 Sine 1 1 Cotang. 1 Tang. jM.j 80 Degrees. 28 (10 Degrees.) a TABLE OF LOGARITHMIC ]m! I .Sine 1 D. 1 Cosine | D. i Tang. 1 D. 1 Cotang. 1 "o 9.23967C ) 1193 9.99336] 37 9.24631S 1230 10.753681 60 1 240386 1191 99332S 37 24705*/ 1228 752943 59 2 241101 1189 99330? 37 247794 1226 752206 58 3 241814 1187 993285 37 24853C 1224 75147G 57 4 242526 1185 993262 37 249264 1222 750736 56 5 243237 1183 993240 37 249998 1220 750002 55 6 243947 1181 993217 38 25073C 1218 749270 54 7 244656 1179 993195 38 251461 1217 748539 53 8 245363 1177 993172 38 252191 1215 747809 52 9 246069 1175 993149 38 252920 1213 747080 51 10 11 246775 9.247478 1173 1171 993127 38 38 253648 1211 746352 50 49 9.993104 9.254374 1209 10.745626 12 248181 1169 993081 38 255100 1207 744900 48 13 248883 1167 993059 38 255824 1205 744176 47 14 249583 1165 993036 38 256547 1203 743453 46 15 250282 1163 993013 38 257269 1201 742731 45 16 250980 1161 992990 38 257990 1200 742010 44 17 251677 1159 992967 38 258710 1198 741290 43 18 252373 1158 992944 38 259429 1196 740571 42 19 253067 1156 992921 38 260146 1194 739854 41 20 21 253761 1154 992898 38 38 260863 1192 739137 40 39 9.254453 1152 9.992875 9.261578 1190 10.738422 22 255144 1150 ' 992852 38 262292 1189 737708 38 23 255834 1148 992829 39 263005 1187 736995 37 24 256523 1146 992806 39 263717 1185 736283 36 25 257211 1144 992783 39 264428 1183 735572 35 26 257898 1142 992759 39 265138 1181 734862 34 27 258583 1141 992736 39 265847 1179 734153 33 28 259268 1139 992713 39 266555 1178 733445 S2 29 259951 1137 992690 39 267261 1176 732739 31 30 31 260633 1135 1133 992666 9.992643 39 39 267967 1174 732033 30 29 9.261314 9.268671 1172 10.731329 32 261994 1131 992619 39 269375 1170 730625 28 33 262673 1130 992596 39 270077 1169 729923 27 34 263351 1128 992572 39 270779 1167 729221 26 35 264027 1126 992549 39 271479 1165 728521 25 36 264703 1124 992525 39 272178 1164 727822 24 37 265377 1122 992501 39 272876 1162 727124 23 38 266051 112'a 992478 40 273573 1160 726427 22 39 266723 1119 992454 40 274269 1158 725731 21 40 267395 1117 992430 40 40 274964 1157 725036 20 19 .41 42 '43 9.268065 1115 9.992406 9.275658 1155 10.724342 268734 1113 992382 40 276351 1153 723649 18 269402 1111 992359 40 277043 1151 722957 17 44 270069 1110 992335 40 277734 1150 722266 16 45 270735 1108 992311 40 278424 1148 721576 15 46 271400 1106 992287 40 279113 1147 720887 14 47 272064 1105 992263 40 279801 1145 720199 13 48 272726 1103 992239 40 280488 1143 719512 12 49 273388 1101 992214 40 281174 1141 718826 11 50 51 274049 9.274708 1099 992190 40 40 281858 9.282542 1140 718142 10 9 1098 9.992166 1138 10.717458 52 275367 1096 992142 40 283225 1136 716775 8 53 276024 1094 992117 41 283907 1135 716093 7 54 276681 1092 992093 41 284588 1133 715412 6 55 277337 1091 992069 41 285268 1131 714732 5 56 277991 1089 992044 41 285947 1130 714053 4 57 278644 1087 992020 41 286624 1128 713376 3 58 279297 1086 991996 41 287301 1126 712699 2 59 279948 1084 991971 41 287977 1125 712023 1 60 280599 1082 9919471 41 288652 1123 711348 0| . 1 Cosine | | Sine 1 1 Cotang. 1 1 Tang. 1 M. j 79 Degrees. SINES AND TANGENTS . (11 Degrees. ) 29 M. 1 Sine 1 D. 1 Cosirre | 1>. 1 Tang;. 1 D- 1 ^ot..i. 1 -] T 9.280599 1082 9.991947 41 9.288652 1123 10.711348 1 60 1 281248 1081 991922 41 289326 1122 710674 59 2 281897 1079 991897 41 289999 1120 710001 58 3 282544 1077 991873 41 290671 1118 709329 57 4 283190 1076 991848 41 291342 1117 708658 56 5 283836 1074 991823 41 292013 1115 707987 55 6 284480 1072 991799 41 292682 1114 707318 54 7 285124 1071 991774 42 293350 1112 706650 53 8 285766 1069 991749 42 294017 1111 705983 52 9 286408 1067 991724 42 294684 1109 705316 51 10 11 287048 9.287687 1066 991699 9.991674 42 42 295349 1107 704651 50 49 1064 9.296013 1106 10.703987 12 288326 1063 991649 42 296677 1104 703323 48 13 288964 1061 991624 42 297339 1103 702661 47 14 289600 1059 991599 42 298001 1101 701999 46 15 290236 1058 991574 42 298662 1100 701338 45 16 290870 1056 991549 42 299322 1098 700678 44 17 291504 1054 991524 42 299960 1096 700020 43 18 292137 1053 991498 42 300638 1095 699362 42 19 292768 1051 991473 42 301295 1093 698705 41 20 293399 1050 991448 42 301961 1092 698049 40 21 9.294029 1048 9.991422 42 9.302607 1090 10.697393 39 22 294658 1046 991397 42 303261 1089 696739 38 23 29528G 1045 991372 43 303914 1087 696086 37 24 295913 1043 991346 43 304567 1086 695433 36 25 296539 1042 991321 43 305218 1084 694782 35 26 297164 1040 991295 43 305869 1083 694131 34 27 297788 1039 991270 43 306519 1081 693481 33 28 298412 1037 991244 43 307168 1080 692832 32 29 299034 1036 991218 43 307815 1078 692185 31 30 299655 1034 991193 43 308463 1077 691537 30 31 9.300276 1032 9.991167 43 9.309109 1075 10.690891 29 32 300895 1031 991141 43 309754 1074 690246 28 33 301514 1029 991115 43 310398 1073 689602 27 34 302132 1028 991090 43 311042 1071 688958 26 35 302748 1026 991064 43 311685 1070 638315 25 36 303364 1025 991033 43 31232?" 1038 687673 24 37 303979 1023 991012 43 312967 1067 687033 23 :38 304593 1022 990986 43 313608 1005 686392 22 39 305207 1020 990960 43 314247 1064 685753 2i 40 305819 1019 990934 44 314885 1062 685il5 20 41 9.306430 1017 9.990908 44 9.315523 1061 10.68MW 19 42 307041 1016 990882 44 316159 1060 683841 18 43 307650 1014 990855 44 316795 1058 683205 i7 44 308259 1013 990829 44 317430 1057 682570 16 45 308867 1011 9908031 44 318064 1055 681936 15 46 309474 1010 990777 44 318697i 1054 681303 14 47 310080 1008 990750 44 3193291 1053 680671 13 48 310685 1007 990724 44 31996l! 1051 680039 12 49 311289 1005 990697 44 3205921 1050 679408 11 50 51 311893 9.312495 1004 990671 44 1 9.990644 44 i 321222: 9.3218511 1048 678778 10 9 1003 1047 10.678149 52 313097 1001 990618 441 322479 1045 677521 8 53 313698 1000 990591 44 i 323106 1044 676894 7 54 314297 998 990565 44 1 323733 1043 6762671 6 55 314897 997 990538 44 324358 1041 675642 5 56 315495 996 990511 45 324983 1040 675017 4 57 316092 994 990485 45 325607 1039 674393 3 58 316689 993 990458 45 326231 1037 673769 2 59 317284 991 990431 45 326853 1036 ! 673147 1 60 317879 990 990404 45 327475 1035 672525 1 Cosine Tang. 78 Degrees. 30 (12 Degrees.) a TABLE OF LOGARlTHillC T| Siii? D. Cosine | D. 1 Tang. D. <-olai!f. I 1 9.317879 990 9.990404 45 9.327474 1035 10.672526 60 1 1 318473 988 990378 45 328095 1033 671905 59 2 319066 987 990351 45 328715 1032 671285 58 3 319658 986 990324 45 329334 1030 670666 57 4 320249 984 990297 45 329953 1029 670047 66 5 320840 983 990270 45 330570 1028 669430 55 6 321430 982 990243 45 331187 1026 668813 54 7 322019 980 990215 45 331803 1025 668197 63 8 322607 979 990188 45 332418 1024 667582 62 9 323194 977 990161 45 333033 1023 666967 51 10 11 323780 976 975 990134 9.990107 45 46 333646 1021 666354 50 49 9.324366 9.334259 1020 10.665741 13 324950 973 990079 46 334871 1019 665129 48 13 325534 972 990052 46 335482 1017 664518 47 14 326117 970 990025 46 336093 1016 663907 46 15 326700 969 989997 46 336702 1015 663298 45 16 327281 968 989970 46 33731 1 1013 662689 44 17 327862 966 989942 46 337919 1012 662081 43 18 328442 965 989915 46 338527 1011 661473 42 19 329021 964 989887 46 339133 1010 660867 4i 20 21 329599 962 989860 46 46 339739 9.340344 1008 1007 660261 10.659656 40 39 9.330176 961 9.989832 22 330753 960 989S04 46 340948 1006 659052 38 23 331329 958 989777 46 341552 1004 658448 37 24 331903 957 989749 47 342155 1003 657845 36 25 332478 956 989721 47 342757 1002 657243 35 26 333051 954 989693 47 343358 1000 656642 34 27 333624 953 989665 47 343958 999 656042 33 28 334195 952 989637 47 344558 998 655442 32 29 334766 950 989609 47 345157 997 654843 31 30 31 335337 949 989582 9.989553 47 47 345755 9.346353 996 994 654245 30 29 9.335906 948 10.653647 32 336475 946 989525 47 346949 993 653051 28 33 337043 945 989497 47 347545 992 652455 27 34 337610 944 989469 47 348141 991 651859 20 35 .338176 943 989441 47 348735 990 661265 25 36 338742 941 989413 47 349329 988 650671 24 37 339306 940 989384 47 349922 987 650078 23 38 339871 939 989356 989328 47 350514 986 649486 22 39 340434 937 47 351106 985 648894 21 40 41 340996 936 989300 9.989271 47 47 351697 983 982 648303 20 19 ^.341558 935 9.352287 10.647713 42 342119 934 989243 47 352876 981 647124 18 43 342679 932 989214 47 353465 9fc0 646535 17 44 343'>^9 931 989186 47 354053 979 645947 16 45 343797 930 989157 47 354640 977 645360 15 46 344365 929 989128 48 355227 976 644773 14 47 344912 927 989100 48 355813 975 644187 13 48 345469 926 989071 48 356398 974 643602 12 49 346024 925 989042 48 356982 973 643018 11 50 346579 924 989014 48 357566 971 642434 10 51 9.347134 922 9.988985 48 9.358149 970 10.641851 9 52 347687 921 988956 48 358731 969 641269 8 53 348240 920 988927 48 359313 968 640687 7 54 348792 919 988898 48 359893 967 640107 6 55 349343 917 988869 48 360474 966 639526 5 56 349893 916 988840 48 361053 965 638947 4 57 350443 915 988811 49 361632 963 638368 3 58 350992 914 988782 49 362210 962 637790 2 59 351540 913 988753 49 362787 961 637213 1 60 352088 1 911 988724 49 363364 960 636f;36 t'OritirT 1 1 Sine 1 1 <■,»:.. 1 T..g |M] 77 Degrees. SINES AND TANGENTS. (13 Degrees.) 31 IVI 1 Sine 1 D. } Cosine 1 1). 1 Ta.., 1 '^ 1 C.>,.ar., 1 ^ 9.352088 911 9.988724 49 9.363364 900 10.636636 60 1 352635 910 98S695 918666 49 363940 959 636060 59 2 353181 909 49 364515 958 635485 58 3 353726 908 988636 49 365090 957 634910 57 4 354271 907 988607 49 365664 955 634336 56 5 354815 905 988578 49 368237 954 633763 55 6 355358 904 988548 49 366810 953 633190 54 7 355901 903 988519 49 367382 952 632618 53 8 356443 902 988489 49 367953 951 633047 52 9 356984 901 988460 49 363524 950 631476 51 10 11 357524 899 988430 9.988401 49 49 369094 949 630906 10.630337 50 49 9.358064 898 9.369663 948 12 358603 897 988371 49 370232 946 629768 48 13 359141 896 988342 49 370799 945 629201 47 14 359678 895 988312 50 371367 944 628333 46 15 360315 S93 9882-3 50 371933 943 628067 45 16 360752 892 988252 50 372499 942 627501 44 17 361287 891 988223 50 373064 941 623936 43 18 361822 S90 988193 50 373829 940 62G371 42 19 36235S 889 988163 50 374193 * 939 625307 41 20 21 362889 9.363422 88S 988133 9.988103 50 50 374756 938 625344 40 39 887 9.375319 937 10.624681 22 363954 885 988073 50 375881 935 624119 33 23 364485 884 988043 50 376442 934 623558 37 24 365016 8--3 988013 50 377003 933 623997 36 25 365546 882 987983 50 377563 932 622437 35 26 366075 881 937953 50 378122 931 621378 34 27 396604 880 987922 50 378Gs:! 930 62131^ 33 28 367131 879 987892 50 379239 929 620 76 1 32 29 367659 877 937862 50 379797 928 620<;03 31 30 31 368185 9.368711 873 875 987-332 9.937801 51 51 3803 H 9.3S09.U 927 619546 30 29 923 1O.6J909O 32 369236 874 987771 51 381463 925 618534 28 33 369761 873 987740 51 333020 924 617980 27 34 370285 872 987710 51 332575 923 617425 26 35 370808 871 987679 51 383129 922 616371 25 36 371330 870 987649 51 333632 921 616318 24 37 371852 869 987618 51 384234 920 615766 23 38 372373 867 987588 51 334736 919 615214 22 39 372894 866 987557 51 335337 918 614363 21 40 41 373414 865 987526 9.987496 51 51 335333 917 61413 2 20 19 9.373933 864 9,386433 915 10.613562 42 ,374452 863 987485 51 3869'!7 914 613013 18 43 374970 862 987434 51 337536 913 612164 17 44 3754S7 861 987403 52 388034 912 rii9i3 16 45 376003 860 987372 52 383331 911 611369 15 46 376519 859 987341 52 389173 910 610322 14 47 377035 858 997310 52 389724 909 610276 13 48 377549 857 987279 52 390270 908 609730 12 49 378063 856 987248 52 390815 907 609135 11 50 51 378577 854 987217 52 52 391360 906 603640 10. 603097 10 9 9.379089 853 9.987186 9.391903 905 52 379601 852 987155 52 392447 904 607553 8 53 380113 851 987124 52 392939 903 607011 7 54 380624 850 987092 52 393531 902 606469 6 55 381134! 849 987061 52 394073 901 605927 5 56 381643 84S 987030 52 394614 900 605386 4 57 382152 847 986998 52 395154 899 604846 3 58 382661 846 986967 52 395694 898 6043031 2 59 383168 845 986936 52 396233 897 6037671 I 60 383675 844 986904 52 396771 896 603229' «: _1 r :. 1 1 s.. , , Oniai..- 1 1 ... |V.| 76 Degrees. 32 (14 Degrees.) a table of logarithmic ir\ Sine 1 D. 1 Cosine | D. Tang. 1 D. 1 Cotang. 1 \ 9.383675 844 ! 9.986904 52 9.396771 896 10.603229 60 1 384182 843 986873 53 397309 3ar846 896 602691 59; 2 384687 842 986841 53 895 602154 58 3 385192 841 986809 53 398.383 894 601617 57 4 385697 840 986778 53 398919 893 601081 56 5 386201 839 986746 53 399455 892 600545 55 6 386704 838 986714 53 399990 891 600010 54 7 387207 837 986683 53 400524 890 599476 53 8 387709 836 986651 53 401058 889 598942 52 9 388210 835 986619 53 401591 888 598409 51 10 11 388711 834 986587 9.986555 53 53 402124 887 597876 50 49 9.389211 833 9.402656 886 10.597344 12 13 14 389711 832 986523 53 403187 885 596813 48 390210 831 986491 53 403718 884 596282 47 390708 830 986459 53 404249 883 595751 46 il5 391206 828 986427 53 404778 882 595222 45 16 391703 827 986395 53 405308 881 594692 44 17 392199 826 986363 54 405836 880 594164 43 18 392695 825 986331 54 406364 879 593636 42 19 393191 824 986299 54 406892 878 593108 41 20 393685 9.394179 823 986266 9.986234 54 54 407419 877 592581 40 39 21 822 9.407945 876 10.592055 22 394673 821 986202 54 408471 875 591529 38 23 395166 820 986169 54 408997 874 591003 37 24 395658 819 986137 54 409521 874 590479 36 25 396150 818 986104 54 410045 873 589955 35 26 396641 817 986072 54 410569 872 589431 34 27 397132 S17 986039 54 411092 871 588908 33 2S 397621 816 986007 54 411615 870 588385 32 29 398111 815 985974 54 412137 869 587863 31 30 31 398600 , 814 985942 9.985909 54 55 412658 868 587342 30 29 9.399088 ; 813 9.413179 867 10.586821 32 399575 812 985876 55 413699 866 586301 28 33 400062 811 985843 55 414219 865 585781 27 34 400549 810 985811 55 414738 864 585262 26 35 401035 809 985778 55 415257 864 584743 25 36 401520 808 985745 55 415775 863 584225 24 37 402005 807 985712 55 416293 862 683707 23 38 402489 806 985679 55 416810 861 583190 22 33 402972 805 985646 55 417326 860 582674 21 40 41 403455 804 985613 55 55 417842 859 582158 20 19 9.403938 803 9.985580 9.418358 858 10.581642 42 404420 802 985547 55 418873 857 581127 18 43 404901 801 985514 55 419387 856 580613 17 44 405382 800 985480 55 419901 855 580099 16 45 405862 799 985447 55 420415 855 579585 15 46 406341 1 798 985414 56 420927 854 579073 14 47 406820 1 797 985380 56 421440 853 578560 13 48 407299 ! 796 985347 56 421952 852 578048 12 49 407777 795 985314 56 422463 851 577537 11 50 51 408254 794 985280 9.985247 56 56 422974 850 577026 10 9 9.408731 i 794 9.423484 849 10.576516 52 40920'} ''\ 793 985213 56 423993 848 576007 8 53 40968S ,: 792 985180 56 424503 848 575497 7 54 41015'; ^j 791 985146 56 425011 847 574989 6 55 41063S 5' 790 985113 56 425519 846 574481 5 56 41110C )i 789 985079 56 426027 845 ,573973 4 57 411571 y 788 985045 56 428534 844 573466 3 58 412055 I 787 985011 56 427041 843 572959 2 59 41252^ I 786 984978 56 427547 84;^ 572453 1 60 1 41299( 5 785 984944 56 428052 842 571948 1 Tv^ine Sine I Tang. 75 Degrees. SINES AND TANGENTS. (15 Degrees.) 33 M, ] Siue 1 D- 1 Cosine 1 D. 1 Taiiij. i D. i Cota=. 1 1 ==0 9.412996 785 9.984944 57 9.428052 842 10.571948 60 1 413467 784 984910 57 428557 841 571443 59 2 413938 783 984876 57 429062 840 570938 58 3 414408 783 984842 57 429566 839 570434 57 4 414878 782 984808 57 430070 838 569930 56 5 415347 781 984774 57 430573 838 569427 55 6 415815 780 984740 57 431075 837 568925 54 7 416283 779 984706 57 431577 836 568423 53 8 416751 778 984672 57 432079 835 567921 52 9 417217 777 984637 57 432580 834 567420 51 10 11 417684 776 775 984603 9.984569 57 57 433080 833 566920 50 49 9.418150 9.433580 832 10.566420 12 418615 774 984535 57 434080 832 565920 48 13 419079 773 984500 57 434579 831 565421 47 14 419544 773 984466 57 435078 830 564922 46 15 420007 772 984432 58 435576 829 564424 45 16 420470 771 984397 58 436073 828 563927 44 17 420933 770 984363 58 436570 828 563430 43 18 421395 769 984328 58 437067 827 562933 42 19 421857 768 984294 58 437563 826 562437 41 20 21 422318 9 422778 767 767 984259 58 58 438059 825 824 561941 10.561446 40 39 9.984224 9.438554 22 423238 766 984190 58 439048 823 560952 38 23 423697 765 984155 58 439543 823 560457 37 24 424156 764 984120 58 440036 822 559964 36 25 424615 763 984085 58 440529 821 559471 35 26 425073 762 984050 58 441022 820 558978 34 27 425530 761 984015 58 441514 819 558486 33 28 425987 760 983981 58 442006 819 557994 32 29 426443 760 983946 58 442497 818 557503 31 30 31 426899 759 983911 9.983875 58 58 442988 817 557012 10.556521 30 29 9.427354 758 9.443479 816 32 427809 757 983840 59 443968 816 556032 28 33 428263 756 983805 59 444458 815 655542 27 34 428717 755 983770 59 444947 814 555053 26 35 429170 754 983735 59 445435 813 554565 25 36 429623 753 983700 59 445923 812 554077 24 37 430075 752 983664 59 446411 812 553589 23 38 430527 752 983629 59 446898 811 553102 22 39 430978 751 983594 59 447384 810 552616 21 40 41 431429 9.431879 750 983558 9.983523 59 59 447870 9.448356 809 809 552130 20 19 749 10.551644 42 432329 749 983487 59 448841 808 551159 18 43 432778 748 983452 59 449326 807 550674 17 44 433226 747 983416 59 449810 806 550190 16 45 433675 746 983381 59 450294 806 549706 15 46 434122 745 983345 59 450777 805 549223 14 47 434569 744 983309 59 451260 804 548740 13 48 435016 744 983273 60 451743 803 648257 12 49 435462 743 983238 60 452225 802 647775 11 50 51 435908 9.436353 742 983202 60 60 452706 802 547294 10.546813 10 9 741 9.983166 9.453187 801 52 436798 740 983130 60 453668 800 546332 8 53 437242 740 983094 60 454148 799 545852 7 54 437686 739 983058 60 454628 799 545372 6 55 438129 738 983022 60 455107 798 544893 5 56 438572 737 982986 60 455586 797 644414 4 57 439014 736 982950 60 456064 796 543936 3 58 439456 736 982914 60 456542 796 643458 2 59 439897 735 982878 60 457019 795 642981 1 60 440338 734 982842 60 457496 794 542504 1 Cosine j 1 S,„e 1 , Cotang. j I Tap? j ^" 74 E 34 (16 Degrees.) a TABLE or LOGARITHMIC T" Sine 1 D. Cosine | D. \ Ta::2 1 D. 1 Cotari? 1 1 9.440338 734 9.982842! 60 | 9.457496 794 10.542504 60 1 440778 733 982805| 60 457973 793 542027 59 2 441218 732 982769 61 458449 793 541551 58 3 441658 731 982733 61 458925 792 541075 57 4 442096 731 982696 61 459400 791 540600 56 5 442535 730 982660 61 459875 790 540125 55 6 442973 729 982624 61 460a49 790 539651 54 7 443410 728 982587 61 460823 789 539177 53 8 443847 727 982551 61 461297 788 538703 52 9 444284 727 982514 61 461770 788 538230 tl 10 11 444720 726 982477 9.982441 61 61 462242 9.462714 787 786 537758 i 10.537286 50 49 9.445155 725 12 445590 724 982404 61 463186 785 536814 48 13 446025 723 982367 61 463658 785 536342 47 14 446459 723 982331 61 464129 784 535871 46 15 446893 722 982294 61 464599 783 535401 45 16 447326 721 982257 61 465069 783 534931 44 17 447759 720 982220 62 465539 782 534461 43 18 448191 720 982183 62 466008 781 533992 42 19 448623 719 982146 62 466476 780 533524 41 20 21 449054 718 982109 62 62 466945 780 533055 10.532587 40 39 9.449485 717 9.982072 9.467413 779 22 449915 716 982035 62 467880 778 532120 38 23 450345 716 981998 62 468347 778 531653 37 24 450775 715 981961 62 468814 777 531186 36 25 451204 714 981924 62 469280 776 530720 35 26 451632 713 981886 62 469746 775 5302.54 34 27 452060 713 981849 62 470211 775 529789 33 28 452488 712 981812 62 470676 774 529324 32 29 452915 711 981774 62 471141 773 528859 31 30 31 453342 710 981737 9.981699 62 63 471605 9.472068 773 528395 10.527932 30 29 9.453768 710 772 32 454194 709 981662 63 472532 771 527468 28 S3 454619 708 981625 63 472995 771 527005 27 S4 455044 707 981587 63 -473457 770 526543 26 85 455469 707 981549 63 473919 769 526081 25 36 455893 706 981512 63 474381 769 525619 24 37 456316 705 981474 63 474842 768 525158 23 38 456739 704 981436 63 475303 767 524697 22 39 457162 704 981399 63 475763 767 524237 21 40 457584 703 981361 63 476223 766 523777 20 41 9.458006 702 9.981323 63 9.476683 765 10.523317 19 42 458427 701 981285 63 477142 765 522858 18 43 458848 701 981247 63 477601 764 522399 17 44 459268 700 981209 63 478059 763 521941 16 45 459688 699 981171 63 478517 763 521483 15 46 460108 698 981133 !64 478975 762 521025 14 47 460527 698 981095 64 479432 761 530568 13 48 460946 697 9810.57 64 479889 761 520111 12 49 461364 696 981019 64 480345 760 519655 11 50 51 461782 695 980981 64 64 480801 759 519199 10.518743 lio 9 9.462199 695 9.980942 9.481257 759 52 462616 694 980904 64 481712 758 518288 8 53 463032 693 980866 64 482167 757 517833 7 54 463448 693 980627 ! 64 482621 757 517379 6 65 463864 692 9807S9 i64 483075 756 516925 5 56 464279 691 980750 ' 64 483529 755 1 516471 4 57 464694 690 9«f;--12 ■ 64 483982 755 i 516018 3 5S 465108 690 980673 :64 484435 754 515565 2 59 465522 689 980635 64 484887 7.'3 515113 1 60 465935 ' 688 980596 64 485339 753 ^Tr^(^^ I Cosine I I Colans I Tang. j M. 73 Degrees SINES AND TANGENTS. (17 Degrees .) 35 M. .,.,. D. Cosine | D. 1 Tai.g. D. Coiang. 9.465935 688 9.980596 64 9.485339 755 10.514661 60 1 466348 688 980558 64 485791 752 514209 59 2 466761 687 980519 65 486242 751 513758 58 3 467173 686 980480 65 486693 751 513307 57 4 467585 685 980442 65 487143 750 512857 56 5 467996 685 980403 65 487593 749 512407 55 6 468407 684 980364 65 488043 749 511957 54 7 468817 683 980325 65 488492 748 511508 53 8 469227 683 980286 65 488941 747 511069 52 9 469637 682 980247 65 489390 747 510610 51 10 11 470046 681 980208 9.980169 65 65 489838 9.490286 746 510162 10.509714 50 49 9.470455 680 746 12 470863 680 980130 65 490733 745 509267 48 13 471271 679 980091 65 491180 744 508820 47 14 471679 678 980052 65 491627 744 508373 46 15 472086 678 980012 65 492073 743 507927 45 16 472492 677 979973 65 492519 743 507481 44 17 472898 676 979934 66 492965 742 507035 43 18 473304 676 979895 66 493410 741 506590 42 19 473710 675 979855 66 493854 740 506146 41 20 21 474115 674 979816 66 66 494299 9.494743 740 505701 10.505257 40 39 9.474519 674 9.979776 740 22 474923 673 979737 66 496186 739 604814 38 23 475327 672 979697 66 495630 738 504370 37 24 475730 672 979658 66 496073 737 503927 36 25 476133 671 979618 66 49G515 737 503485 35 26 476536 670 979579 66 496957 736 503043 34 27 476938 669 979539 66 497399 736 502601 33 28 477340 669 979499 66 497841 735 5021.59 32 29 477741 668 979459 66 498282 734 501718 31 30 31 478142 667 667 979420 9.979380 66 66 498722 734 733 501278 10.500837 30 29 9.478542 9.499163 32 478942 666 979340 66 499603 733 500397 28 33 479342 665 979300 67 500042 732 499958 27 34 479741 665 979260 67 500481 731 499519 26 35 480140 664 979220 67 500920 731 499080 25 36 480539 663 979180 67 501359 730 498641 24 37 480937 663 979140 67 501797 730 498203 23 38 481334 662 979100 67 502235 729 497755 22 39 481731 661 979059 67 502672 728 497328 21 40 41 482128 661 979019 67 67 503109 728 496891 20 19 9.482525 660 9.978979 9.503546 727 10.496454 42 482921 659 978939 67 503982 727 496018 18 43 48.3316 659 978898 67 504418 726 495582 17 44 483712 658 978858 67 504854 725 495146 16 45 484107 657 978317 67 •505289 725 494711 15 46 484501 657 978777 67 505724 724 494276 14 47 484895 656 978736 67 506159 724 493841 13 48 485289 655 978696 68 506593 723 493407 12 49 485682 655 978655 68 507027 722 492973 11 50 51 486075 654 978615 68 68 507460 9.507893 722 721 492540 10 9 9.486467 653 9.978574 10.492107 52 486860 653 978533 68 508326 721 491674 8 53 487251 652 978493 68 508759 720 491241 7 54 487643 651 978452 68 509191 719 490809 6 55 488034 651 978411 68 509622 719 490378 5 56 488424 650 978370 68 5100.54 718 489946 4 57 488814 650 978329 68 510485 718 489515 3 58 489204 649 978288 68 510916 717 489084 2 59 489593 648 978247 68 511346 716 488654 1 60 489982 648 978206 68 511776 716 488224 t n Cosine | 1 Sine 1 1 Cotanif. j ■ia„g. |M.I 72 Degrees, 36 (18 Degrees.) a TABLE or LOGARITHMIC M. 1 Sine j P. \ Cosine | D Tang. 1 D 1 Coiang. I 1 9.489982 648 9.978206 68 ( 9.5U776I 716 10.488224 60 1 490371 648 978165 68 512206i 716 487794 59 2 490759 647 978124 68 5126.351 715 487365 58 3 4911471 646 978083 69 513064 714 486936 57 4 491535 646 978042 69 513493 714 486507 56 5 491922 645 978001 69 513921 713 486079 55 6 4923081 644 977959 69 514349 713 485651 54 7 4926951 644 977918 69 514777 712 485223 53 8 493081; 643 977877 69 515204 712 484796 52 9 493466 642 977835 69 515631 711 484369 51 10 11 493851 1 642 977794 9.977752 69 69 516057! 710 483943 10.483516 50 49 9.4942361 641 9.516484 710 12 494621 641 977711 69 516910) 709 483090 48 13 495005 640 977669 69 517335! 709 482665 47 14 495388 639 977628 69 5177611 708 482239 46 15 495772! 639 977586 69 518185 708 481815 45 16 4961541 638 977544 70 518610! 707 481390 44 17 496537 637 977503 70 5190341 706 480966 43 18 496919 637 977461 70 5194581 706 480542 42 19 497301 636 977419 70 519882 705 480118 41 20 21 497682 636 977377 9.977335 70 70 520305 705 479695 10.479272 40 39 9.498064 635 9.520728 704 22 498444 634 977293 70 521151 703 478849 38 23 498825 634 977251 70 521573 703 478427 37 24 499204 633 977209 70 521995 703 478005 36 25 499584 632 977167 70 522417 702 477583 35 26 499963 632 977125 70 522838 702 477162 34 27 500342 631 977083 70 523259 701 476741 33 28 500721 631 977041 70 523680 701 476320 32 29 501099 630 976999 70 524100 700 475900 31 30 31 501476 629 976957 70 70 524520 699 699 475480 30 29 9.501854 629 9.976914 9.524939 10.475061 32 502231 628 976872 71 525359 698 474641 28 33 502607 628 976830 71 525778 698 474222 27 34 502984 627 976787 71 526197 697 473803 26 35 603360 626 976745 71 526615 697 473385 25 36 503735 626 976702 71 527033 896 472967 24 37 504110 625 976660 71 527451 696 472549 23 38 504485 625 976617 71 527868 695 472132 22 39 504860 624 976574 71 528285 695 471715 21 40 41 505234 623 976532 71 71 528702 694 471298 0.470881 20 19 9.505608 623 9.976489 9.529119 693 42 505981 622 976446 71 529535 693 470465 18 43 506354 622 976404 71 529950 693 470050 17 44 506727 621 976361 71 530366 692 469634 16 45 507099 620 976318 71 530781 691 469219 15 46 507471 620 976275 71 531196 691 468804 14 47 507843 619 976232 72 531611 690 468389 13 48 508214 619 976189 72 532025 690 467975 12 49 508585 618 976146 72 532439 689 467561 11 50 51 508956 618 976103 72 72 532853 689 467147 10 9 9.509326 617 9.976060 9.533266 688 10.466734 52 509696 616 976017 72 533679 688 466321 8 53 510065 616 975974 72 534092 687 465908 7 54 510434 615 975930 72 534504 687 465496 6 55 510803 615 97588? 72 534916 686 465084 5 56 511172 614 975844 72 535328 686 464672 4 57 511540 613 975800 72 535739 685 464261 3 58 511907 613 975757 72 536150 685 463850 2 59 512275 612 975714 72 536561 684 463439 1 60 512642 612 975670 72 536972 684 463028 ^ 1 Cosine | 1 Sine 1 1 Cotan^. 1 1 Tang. ( M. 71 Degrees. SINES a:sd tangents. (19 Degrees .) 37 nn Sine 1 D. 1 Cosine D. 1 Tang. 1 D. 1 Cotang. 1 9.512642 612 9.975670 73 9.536972 684 10.463028 60 1 513009 611 975627 73 537382 683 462618 59 2 513375 611 975583 73 537792 683 462208 58 3 513741 610 975539 73 638202 682 461798 57 4 514107 609 975496 73 538611 682 461389 66 5 514472 609 975452 73 539020 681 460980 56 6 514837 608 975408 73 539429 681 460571 54 7 515202 608 975365 73 539837 680 460163 53 8 515566 607 975321 73 540245 680 459755 52 9 515930 607 975277 73 540653 679 459347 51: 10 11 516294 9.516657 606 605 976233 73 73 541061 679 458939 10.458532 50 49 9.975189 9.541468 678 12 517020 605 976145 73 641875 678 458125 48 13 517382 604 975101 73 542281 677 457719 47 14 517745 604 975057 73 642688 677 457312 46 15 518107 603 975013 73 643094 676 456906 45 16 518468 603 974969 74 543499 676 456501 44 17 518829 602 974925 74 543906 675 456096 43 18 519190 601 974880 74 644310 675 455690 42 t 19 519551 601 974836 74 644716 674 455285 41 20 21 519911 600 974792 74 74 545119 674 454881 10.464476 40 39 9.520271 600 9.974748 9.546524 673 22 520631 599 974703 74 545928 673 454072 38 23 520990 599 974659 74 646331 672 453669 37 24 621349 598 974614 74 646735 672 453265 36 25 521707 598 974670 74 647138 671 452862 35 26 522066 597 974525 74 547640 671 452460 34 27 522424 696 974481 74 647943 670 452057 33 28 522781 696 974436 74 548345 670 451655 32 29 523138 595 974391 74 548747 669 451253 31 30 31 523495 595 974347 9.974302 75 75 549149 669 450851 10.450450 30 29 9.523852 594 9.549550 668 32 624208 694 974257 75 549951 668 450049 28 33 524564 593 974212 75 550352 667 449648 27 34 524920 593 974167 75 650752 687 449248 26 35 525275 692 974122 75 551152 666 448848 25 36 525630 591 974077 75 651552 666 448448 24 37 525984 591 974032 75 651952 665 448048 23 38 626339 590 973987 76 552351 665 447649 22 39 526693 590 973942 75 652750 665 447250 21 40 41 527046 689 973897 76 75 653149 9.553548 664 446851 20 19 9.527400 589 9.973852 664 10.446452 42 527753 588 973807 76 653946 663 446054 18 43 528105 588 973761 75 654344 663 445656 17 44 528458 687 973716 76 654741 662 445259 16 45 528810 587 973671 76 555139 662 444861 16 46 529161 586 973625 76 555536 661 444464 14 47 529513 586 973580 76 565933 661 444067 13 48 529864 685 973535 76 556329 660 443671 12 49 530215 586 973489 76 656725 660 443275 11 50 51 530565 584 973444 76 76 657121 9.567517 659 659 442879 10 9 9.530915 584 9.973398 10.442483 52 531265 583 973352 76 667913 669 442087 8 53 531614 582 973307 76 658308 658 441692 7 54 531963 682 973261 76 568702 658 441298 6 55 532312 581 973215 76 659097 657 440903 5 56 532661 581 973169 76 559491 657 440509 4 57 53300C 580 973124 76 569885 656 440115 3 58 53335< ' 680 973078 76 660279 656 439721 2 59 53370^ 1 679 97303S , 77 560673 655 439327 1 60 534055 I 578 9729861 77 561066 655 438934 H I Cosine 1 1 Sine 1 1 Cotang. 1 1 Tan?. 1 M. j 70 Degrees. 38 (20 Degrees.) a TABLE OF LOGARITHMIC :I. 1 Sine 1 D. 1 Co-ine | D. 1 Tang. i D 1 Cola.^. 1 1 "o" 9.5340521 578 9.972986 77 9.561066 655 10.438934 60 1 534399 577 972940 77 561459 654 438541 59 2 534745 677 972894 77 561851 654 438149 58 3 635092 577 972848 77 662244 653 437756 57 4 535438 676 972802 77 562636 653 437364 56 5 535783 576 972755 77 563028 653 436972 55 6 536129 676 972709 . 77 563419 652 436581 54 7 536474 674 972663 77 663811 652 436189 53 8 536818 574 972617 77 664202 651 435798 52 9 637163 573 972570 77 564692 651 435408 51 10 11 637607 9.637851 573 972524 9.972478 77 77 664983 650 435017 10.434627 50 49 672 9.665373 650 12 638194 672 972431 78 665763 649 434237 48 13 638538 571 972385 78 566153 649 433847 47 14 538880 571 972338 78 566542 649 433458 46 15 639223 670 972291 78 566932 648 433068 45 16 639565 670 972245 78 567320 648 432680 44 17 639907 569 972198 78 567709 647 432291 43 18 640249 569 972151 78 668098 647 431902 42 19 540690 668 972105 79 668486 646 431514 41 20 21 540931 668 972058 78 78 568873 646 431127 40 39 9.641272 667 9.972011 9.569261 645 10.430739 22 541613 567 971964 78 569648 645 430352 38 23 541953 566 971917 78 570035 645 429965 37 24 642293 566 971870 78 670422 644 429578 36 25 64263'2 565 971823 78 670809 644 429191 35 26 542971 565 971776 78 671195 643 428805 34 27 543310 664 971729 79 571581 643 428419 33 28 643649 664 9716S2 79 671967 642 428033 32 29 643987 663 971635 79 572352 642 427648 31 30 31 644^25 663 971588 9.971540 79 79 672738 642 427262 30 29 9.544663 662 9.573123 641 10.426877 32 545000 562 971493 79 673507 641 425493 28 33 545338 561 971446 79 573892 640 426108 27 34 545674 561 971398 79 574276 640 425724 26 35 546011 560 971351 79 574660 639 425340 25 36 646347 560 971303 79 575044 639 424956 24 37 646683 569 971256 79 675427 639 424573 23 38 547019 559 971208 79 675810 638 424] 90 22 39 547364 568 971161 79 576193 638 423807 21 40 41 547689 658 971113 9.971066 79 80 576576 637 423424 20 19 9.548024 557 9.576958 637 10.423041 42 648369 557 971018 80 577341 636 422659 18 43 548693 656 970970 80 577723 636 422277 17 44 549027 656 970922 80 578104 636 421896 16 45 649360 665 970874 80 678486 635 421514 15 46 649693 655 970827 80 578867 635 421133 14 47 550026 564 970779 80 679248 634 420752 13 48 550359 654 970731 80 579629 634 420371 12 49 550692 563 970683 80 580009 634 419991 11 50 51 551024 9.561356 553 970635 80 80 580389 633 419611 10.419231 10 9 652 9.970586 9.580769 633 52 551687 652 970538 80 681149 632 418851 8 53 662018 652 970490 80 581528 632 418472 7 54 662349 551 970442 80 681907 632 418093 6 55 652680 551 970394 80 682286 631 417714 5 56 553010 650 970345 81 582665 631 417335 4 57 553341 650 970297 81 583043 630 416957 3 58 653670 549 970249 81 583422 630 416578 2 59 564000 549 970200 81 583800 629 416200 1 60 5.54329 548 970152 81 584177 629 415823 Cosiue Sine j Cotang. 1 Tang. 1 M. ( €9 Degrees. SINES AND TANGENTS . (21 Degrees.) 39 :-l Sine 1 ... 1 (VM.e 1 D. I Tn... 1 D. 1 < otang. I =r= } . 554329 548 9.970152 81 9.584177 629 10.415823 60 1 554658 548 970103 81 584555 629 415445 59 2 554987 547 970055 81 584932 628 415068 58 3 555315 547 970006 81 585309 628 414691 57 4 555643 546 969957 81 585686 627 4143-14 56 5 555971 546 969909 81 586062 627 413938 55 6 556299 545 969860 81 586439 627 413561 54 7 556626 545 969811 81 586815 626 413185 53 8 556953 544 969762 81 587190 626 412810 52 9 557280 544 969714 81 587566 625 412434 51 10 11 557606 543 969665 81 82 587941 625 412059 50 10.411684 49 9.557932 543 9.969616 9.588316 625 12 558258 543 969567 82 588691 624 411309 48 13 558583 542 969518 82 589066 624 410934 47 14 558909 542 969469 82 589440 623 410560 46 15 559234 541 969420 82 589814 623 410186 45 16 559558 541 969370 82 590188 623 409812 44 17 559883 540 969321 82 590562 622 409438 43 18 560207 540 969272 82 590935 622 409065 42 19 560531 539 969223 82 591308 622 408692 41 20 21 560855 539 969173 82 82 691681 9.592054 621 621 408319 40 9.561178 538 9.969124 10.407946 39 22 561501 538 969075 82 592426 620 407574 38 23 561824 537 969025 82 592798 620 407202 37 24 562146 537 968976 82 593170 619 406829 36 25 562468 536 968926 83 593542 619 406458 35 26 562790 536 968877 83 593914 618 406086 34 27 563112 536 968827 83 594285 618 405715 33 28 563433 535 968777 83 594656 618 405344 32 29 563755 535 968728 83 595027 617 404973 31 30 31 564075 534 968678 9.968628 83 83 595398 9.595768 617 617 404602 30 9.564396 534 10.404232 29 32 564716 533 968578 83 596138 616 403862 28 33 565036 533 968528 83 596508 616 403492 27 34 565356 532 968479 83 596878 616 403122 26 35 565676 532 968429 83 597247 615 402753 25 36 565995 531 968379 83 597616 615 402384 24 37 566314 531 9683.29 83 597985 615 402015 23 38 566632 531 968278 83 598354 614 401646 22 39 566951 530 968228 84 598722 614 401278 21 40 41 567269 530 968178 9.968128 84 84 599091 613 400909 20 10.400541 19 9.567587 529 9.599459 613 42 567904 529 968078 84 599827 613 400173 18 43 568222 528 968027 84 600194 612 399806 17 44 56853S 528 96797? 84 600562 612 399438 16 45 568856 528 967927 84 60092S 611 399071 15 46 569 17S , 527 96787€ 84 601296 611 398704 14 47 56948$ 527 967826 84 601665 611 398338 13 48 56980^ i 526 96777£ ) 84 60202i 610 397971 12 49 570 12( ) 526 96772f » 84 60239: ) 610 397605 11 50 57043i i 525 96767^ t 84 60276] L 610 397239 10 51 9.57075 L 525 9.96762^ i 84 9.60312' r 609 10.396873 9 52 57106 5 524 96757J i 84 60349J J 609 396507 8 53 57138( ) 524 96752' I 85 60385f i 609 396142 7 54 57169 3 523 96747 I 85 60422J J 608 395777 6 55 57200 9 523 96742 1 85 60458^ 3 608 395412 5 56 57232 3 523 96737 3 85 60495 3 607 395047 4 57 57263 6 522 96731 3 85 60531 7 607 394683 3 58 57295 522 96726 3 85 60568 2 607 394318 2 59 57326 3 521 96721 7 85 60604 3 606 393954 1 J60 57357 5 521 96716 8 85 6064K 3 606 393590 I Cosine 1 1 Sine 1 j Cotaiig. 1 j Tang. 1 M. ( 38 Dt .grecs. 40 (22 Degrees.) a TABLE OF L'OGARITHMIC M. 1 Sine 1 D. 1 Cosine | D. 1 Tang. 1 D. 1 Cotang. PI T 9.573575 521 9.967166 85 9.606410 606 10.393590 60 1 573888 520 967115 85 606773 606 393227 59 2 574200 520 967064 85 607137 605 392863 58 3 574512 519 967013 85 607500 605 392500 57 4 574824 519 966961 85 607863 604 392137 56 5 575136 519 966910 85 608225 604 391775 55 6 575447 518 966859 85 608588 604 391412 54 7 575758 518 966808 85 608950 603 391050 53 8 576069 517 966756 86 609312 603 390688 52 9 576379 517 966705 86 609674 603 390326 51 10 11 576689 516 966653 86 86 610036 602 389964 10.389603 50 49 9.576999 516 9.966602 9.610397 602 12 577309 516 966550 86 610759 602 389241 48 13 577618 515 966499 86 611120 601 388880 47 14 577927 515 966447 86 611480 601 388520 46 15 578236 514 966395 86 611841 601 388159 45 16 678545 514 966344 86 612201 600 387799 44 17 578853 513 966292 86 612561 600 387439 43 18 579162 513 966240 86 612921 600 387079 42 19 579470 513 966188 86 613281 599 386719 41 20 21 579777 512 966136 9 966085 86 87 613641 599 386359 10.386000 40 39 9.580085 512 9.614000 598 22 580392 511 966033 87 614359 598 385641 38 23 580699 511 965981 87 614718 598 385282 37 24 581005 511 965928 87 615077 597 384923 36 25 581312 510 965876 87 615435 597 384565 35 26 581618 510 965824 87 615793 597 384207 34 27 581924 509 965772 87 616151 596 383849 33 28 582229 509 965720 87 616509 596 383491 32 29 582535 509 965668 87 616867 596 383133 31 30 31 582840 508 965615 87 87 617224 595 382776 30 29 9.583145 508 9.965563 9 617582 595 10.382418 32 583449 507 965511 87 617939 595 382061 28 33 583754 507 965458 87 618295 594 381705 27 34 584058 506 965406 87 618652 594 381348 26 35 584361 506 965353 88 619008 594 380992 25 36 584665 506 965301 88 619364 593 380636 24 37 584968 505 965248 88 619721 593 380279 23 38 585272 505 965195 88 620076 593 379924 22 39 585574 504 965143 88 620432 592 379568 21 40 41 585877 504 965090 9.965037 88 88 620787 592 379213 10.378858 20 19 9.586179 503 9.621142 592 42 586482 503 964984 88 621497 591 378503 18 43 586783 503 964931 88 621852 591 378148 17 44 587085 502 964879 88 622207 590 377793 16 45 587386 502 964826 88 622561 590 377439 15 46 587688 501 964773 88 622915 590 377085 14 47 587989 501 964719 88 623269 589 376731 13 48 588289 501 964666 89 623623 589 376377 12 49 588590 500 964613 89 623976 589 376024 11 50 51 588890 500 964560 9.964507 89 89 624330 9.624683 588 588 375670 10 9 9.589190 499 10.375317 52 589489 499' 964454 89 625036 588 374964 8 53 589789 499 964400 89 625388 687 374612 7 54 590088 498 964347 89 625741 587 374259 6 55 590387 498 964294 89 626093 587 373907 5 56 590686 497 964240 89 626445 586 373555 4 57 590984 497 964187 89 626797 586 373203 3 58 591282 497 964133 89 627149 686 372851 2 59 591580 496 964080 89 627501 585 372499 1 60 591878 496 964026 89 627852 585 372148 Cosine 1 Sine 1 Cotang. 1 1 Tang. 1 M. | 67 Degress. SINES AND TANGENTS. (23 Degrees.) 41 M. Sine D. Cosine 1 D. Tang. 1 D. Cotang. 1 1 9.591878 496 9.964026 89 9.627852 585 10.372148 60: 1 592176 495 963972 89 628203 585 371797 59; 2 592473 495 963919 89 628554 585 371446 58^ 3 592770 495 963865 90 628905 584 371095 57: 4 593067 494 963811 90 629255 584 370745 56 5 593363 494 963757 90 629606 583 370394 55 6 593659 493 963704 90 629956 583 370044 54 7 593955 493 963650 90 630306 583 369694 53 8 694251 493 963596 90 630656 583 369344 62 9 594547 492 963542 90 631005 582 368995 51 10 11 594842 9.595137 492 963488 90 90 631355 582 368645 50 49: 491 9.963434 9.631704 582 10.368296 12 595432 491 963379 90 632053 581 367947 48; 13 595727 491 963325 90 632401 581 367599 47- 14 596021 490 963271 90 632750 581 367250 46 15 596315 490 963217 90 633098 580 366902 45 16 596609 489 963163 90 633447 580 366553 44 17 .596903 489 963108 91 633795 580 366205 43 18 597196 489 963054 91 634143 579 365857 42 19 597490 488 962999 91 634490 579 365510 41 20 21 597783 488 962945 91 91 634838 579 365162 40 39 9.598075 487 9.962890 9.635185 578 10.364815 22 598368 487 962836 91 635532 578 364468 38 23 598660 487 962781 91 635879 578 364121 37 24 598952 486 962727 91 636226 577 363774 36 25 599244 486 962672 91 636572 577 363428 35 26 599536 485 962617 91 636919 577 36.3081 34 27 599827 485 962562 91 637265 577 362735 33 28 600118 485 962508 91 637611 576 362389 32 29 600409 484 962453 91 637956 576 362044 31 30 31 600700 9.600990 484 484 962398 92 92 638302 9.638647 576 361698 10.361353 30 29 9.962343 575 32 601280 483 962288 92 638992 575 361008 28 33 601570 483 962233 92 639337 575 360663 27 34 601860 482 962178 92 639682 574 360318 26 35 602150 482 962123 92 640027 574 359973 25 36 602439 482 962067 92 640371 574 359629 24 37 602728 481 962012 92 640716 573 359284 23 38 603017 481 961957 92 641060 573 358940 22 39 603305 481 961902 92 641404 573 358596 21 40 41 603594 480 961846 92 92 641747 572 358253 20 19 9.603882 480 9.961791 9.642091 572 10.357909 42 604170 479 961735 92 642434 572 357566 18 43 604457 479 961680 92 642777 572 357223 17 44 604745 479 961624 93 643120 571 356880 16 45 605032 478 961569 93 643463 571 356537 15 46 605319 478 961513 93 643806 571 356194 14 47 605606 478 961458 93 644148 570 355852 13 48 605892 477 961402 93 644490 570 355510 12 49 606179 477 961346 93 644832 570 355168 11 50 51 606465 9.606751 476 961290 93 93 645174 569 354826 10 9 476 9.961235 9.645516 569 10.354484 52 607036 476 961179 93 645857 569 354143 8 53 607322 475 961123 93 646199 569 353801 7 54 607607 475 961067 93 646540 568 353460 6 55 607892 474 961011 93 646881 568 353119 5 56 608177 474 960955 93 647222 568 352778 4 57 608461 474 960899 93 647562 567 352438 3 58 608745 473 960843 94 647903 567 352097 2 59 609029 473 960786 94 648243 567 351757 1 60 609313 473 960730 94 648583 586 361417 Cosine 1 Sine 1 Cotang, 1 1 Tang |>1.| Degrees. F 4a (2'4 Degrees.) a TABLE OF L0GAEITH3UC M Sine 1 D. i'u^^ine 1 D. Tai.g. D. Corang. | | 9.609313 473 9.960730 94 9.648583! 566 10.351417 60 1 609597 472 960674 94 648923' 566 351077 59 2 609880 472 960618 94 649263' 566 350737 58 3 610164 472 960561 94 649602: 566 350398 57 4 610447 471 960505 94 649942! 565 350058 56 6 610729 471 960448 94 650281: 565 349719 55 6 611012 470 960392 94 650620! 565 349380 54 7 611294 470 960335 94 650959: 564 349041 53 8 611576 470 960279 94 651297: 564 34S703 52 9 611858 469 9602221 94 651636, 564 348364 51 10 11 612140 469 960165 9.960109 94 95 651974! 563 348026 10.347688 50 49 9.612421 469 9.652312; 563 12 612702 468 960052 95 652650; 563 347350 48 13 612983 468 959995 95 6529881 563 34 7012 47 14 613264 467 959938 95 653326! 562 . 346674 46 15 613545 467 959882 95 653663! 562 346837 45 Ifi 613825 467 959825 95 6540001 .562 346000 44 17 614105 466 9597«8 95 654337. 561 345663 43 18 614385 466 959711 95 654674 561 345326 42 19 614665 466 959654 95 65501 1! 561 3449 S 9 41 20 21 614944 9.615223 465 465 959596 95 95 6553481 581 344652 40 39 9.959539 9.6556S4i 560 10.344316 22 615502 465 959482 95 6560201 560 343980 38 23 615781 464 959425 95 656356! 560 343644 37 24 616060 464 959368 95 656692^ 559 343308 36 25 616338 464 959310 96 6570->8' 559 342972 35 26 616616 463 959253 96 657364 559 342636 34 27 616894 463 959195 96 657699 559 342301 33 28 617172 462 959138 96 65S034 558 341966 32 :.'9 617450 462 959081 96 658339 558 341631 31 30 31 617727 9.618004 462 959023 96 £6 658704 558 341296 10.340961 30 29 461 9.958965 9.659039 558 32 618281 461 958908 S6 659373 557 340627 28 33 618558 461 958850 96 659708 557 340292 27 34 618834 460 958792 96 660042 557 339953 26 35 619110 460 958734 96 660376 557 339624 25 36 6193S6 460 958677 96 660710 556 339290 24 37 619662 459 958619 96 661043 556 33S957 23 38 619938 459 9585611 9 a 661377 556 338623 22 39 620213 459 958503! 97 661710 555 338290 21 40 41 620488 458 958445 97 ,97 662043 555 337957 20 19 9.620763 • 458 9.958387 9.662376 555 10.337624 42 621038 457 95S;329l 97 662709 5.54 337291 18 43 621313 457 9582^1' 97 663042 554 336958 17 44 621587 457 958215: 97 663375 554 . 336625 16 45 621861 456 958154: b7 663707 5.54 336293 15 46 622135 456 958096 97 664039 553 335961 14 47 622409 456 958038' 97 664371 553 335629 13 48 622682 455 957979; 97 664703 553 335297 12 49 622956 , 455 957921197 665035 553 334965 11 50 51 623229 ' 455 957863! 97 9.957804, 97 665366 552 334634 10.334303 10 9 9.623502 454 9.665697 552 52 623774 i 454 957746 98 666029 552 .333971 8 53 624047 1 454 957687 98 666360 551 333640 7 54 624319 ! 453 957628! 98 666691 551 333309 6 55 624591 i 453 957570; 98 667021 551 332979 5 56 624863 453 957511 98 667352 551 332648 4 57 625135 452 957452 98 667682 550 332318 3 58 625406 452 957393J 98 668013 550 331987 2 59 625677 452 9573351 98 668343 550 331657 1 60 625948 1 451 9572761 98 668672 550 331328 1 CosiT.f- 1 Si . , r-iHP.2 1 ^«-- PM 65 Degrees. SINES AND TANGENTS (25 Degrees. ) 4S mA Sine 1 D. Cosine | P. Taog 1 D. Coiang. 1 I 9.625948 451 9.957276 981 9.668673 550 10.3313271 60 1 626219 451 957217 98" 669002 549 330998 59 2 626490 451 957158 98 669332 549 330668 58 3 626760 450 957099 98 669661 549 330339 57 4 627030 450 957040 98 669991 548 330009 56 5 627300 450 956981 98 670320 548 329680 55 6 627570 449 956921 99 670649 548 329351 54 627840 449 956862 99 670977 548 329023 53 8 628109 449 956803 99 671306 547 328694 52 9 628378 448 956744 99 671634 547 328366 51 10 11 628647 448 956684 9.956625 99 99 671963 547 328037 50 49 9.628916 447 9.672291 547 10.327709 12 629185 447 956566 99 672619 546 327381 48 13 629453 447 956506 99 672947 546 327053 47 14 629721 446 956447 99 673274 546 326726 46 15 629989 446 956387 99 673602 546 326398 45 16 630257 446 956327 99 673929 545 326071 44 17 630524 446 956268 99 674257 545 325743 43 18 630792 445 956208 100 674584 545 325416 42 19 631059 445 956148 100 674910 544 325090 41 20 21 631326 445 956089 100 100 675237 544 324763 40 39 9.631593 444 9.956029 9.675564 544 10.324436 '/i'i 631859 444 955969 100 675890 544 324110 38 'ZS 632125 444 955909 100 676216 543 323784 37 24 632392 443 955849 100 676543 543 323457 36 25 632658 443 955789 100 676869 543 323131 35 26 632923 443 955729 100 677194 543 322806 34 27 633189 442 955669 100 677520 542 322480 33 28 633454 442 955609 100 677846 542 322154 32 29 633719 442 955548 100 678171 542 321829 31 30 31 633984 441 955488 9.955428 100 Tor 678496 9.678821 542 541 321504 ia.321179 30 29 9.634249 441 32 634514 440 955368 101 679146 541 320854 28 33 634778 440 955307 101 679471 541 320529 27 34 635042 440 955247 101 679795 541 320205 26 35 635306 439 955186 101 680120 540 319880 25 36 635570 439 955126 101 680444 540 319556 24 37 635834 439 955065 101 680768 540 319232 23 38 636097 438 955005 101 681092 540 318908 22 39 636360 438 954944 101 681416 539 318584 21 40 41 636623 438 437 954883 9.954823 101 101 681740 9.682063 539 539 318260 20 19 9.636886 10.317937 42 637148 437 954762 101 682387 539 317613 18 43 637411 437 95470 J 101 682710 538 317290 17 44 637673 437 954640 101 683033 538 316967 16 45 637935 436 954579 101 683356 538 316644 15 46 638197 436 954518 102 683679 538 316321 14 47 638458 436 954457 102 684001 537 315999 13 48 638720 435 954396 102 684324 537 315676 12 49 638981 435 954335 102 684646 537 315354 11 50 51 639242 435 954274 9.954213 102 102 684968 9.685290 537 315032 10 9 9.639503 434 536 10.314710 52 639764 434 954152 102 685612 536 314388 8 53 640024 434 954090 102 685934 536 314066 7 54 640284 433 954029 102 686255 536 313745 6 55 640544 433 953968 102 686577 535 313423 5 56 640804 433 953906 102 686898 535 313102 4 57 641064 432 953845 102 687219 535 312781 3 58 641324 432 953783 102 687540 535 31246C 2 59 641584 432 953722 103 687861 534 31213£ 1 60 641842 431 953660 103 688182 534 31181? 1 Cosine 1 1 Sine 1 Colang 1 I Ta«g. 1 M. 64 Degrees. 44 (26 Degrees.) a table of logarithmic M. 1 Sine D. Cosine j D. 1 T..... I'-D. 1 Cotang. 1 1 9.641842 ( 431 9.953660 103 (9.688182! 534 10.311818 "60 1 642101 431 953599 103 688502 534 311498 59 2 642360 431 953537 103 688823 ; 534 311177 58 3 642618 430 953475 103 ' 689143 i 533 310857 57 4 642877 430 953413 103 ' 689463 i 533 310537 56 5 643135 430 953352 103 689783 533 310217 55 6 643393 430 953290 103 690103 1 533 309897 54 7 643650 429 953228 103 690423 533 309577 53 8 643908 429 953166 103 690742 ? 532 309253 52 9 644165 429 953104 103 691062 : 532 308938 51 1^ 644423 428 953042 103 104 691381 532 308619 10.308300 50 49 9.644680 428 9.952980 9.691700 531 12 644936 428 952918 104 692019 531 .307981 48 13 645193 427 952855 104 692338 531 307662 47 14 645450 427 952793 104 692656 , 531 307344 46 15 645706 427 952731 104 692975 531 307025 45 16 645962 426 952669 104 693293 530 306707 44 17 646218 426 952606 104 693612 530 306388 43 18 646474 426 952544 104 693930 , 530 306070 42 19 646729 425 952481 104 694248 : 530 305752 41 20 21 646984 425 952419 104 104 694566 529 305434 10.305117 40 39 9.647240 425 9.952356 9.694883 ': 529 22 647494 424 952294 104 695201 i 529 304799 38 23 647749 424 952231 104 695518 . 529 304482 37 24 648004 424 952168 105 695836 i 529 304164 36 25 648258 424 952106 105 696153 ■ 528 303847 35 26 648512 423 952043 105 696470 ; 528 303530 34 27 648766 423 951980 105 696787 528 303213 33 28 649020 423 951917 105 697103 528 302897 32 29 649274 422 951854 105 697420 527 302580 31 30 31 649527 422 951791 105 105 697736 5:698053 527 527 302264 10.301947 30 29 9.6497S1 422 9.951728 32 650034 422 951665 105 698369 527 301631 28 33 650287 421 951602 105 698685 526 301315 27 34 650539 421 951539 105 699001 526 300999 26 35 650792 421 951476 105 699316 526 300684 25 36 651044 420 951412 105 699632 526 300368 24 37 . 651297 420 951349 106 699947 526 300053 23 38 651549 420 951286 106 700263 525 299737 22 39 651800 419 951222 106 700578 525 299422 21 40 41 652052 419 419 951159 106 106 700893 9.701208 525 524 299107 10.298792 20 19 9.652304 9.951096 42 652555 418 951032 106 701523 524 298477 18 43 652806 418 950968 106 701837 524 298163 17 44 653057 418 950905 106 702152 524 297848 16 45 653308 418 950841 106 702466 524 297534 15 46 653558 417 950778 106 702780 523 297220 14 47 653808 417 950714 106 703095 523 296905 13 48 654059 417 950650 106 703409 523 296591 12 49 654309 416 950586 106 703723 523 296277 11 50 51 654558 416 950522 9.950458 107 107 704036 522 295964 10.295650 10 9 9.654808 416 9.704350 522 52 655058 416 950394 107 704663 522 295337 8 53 655307 415 950330 107 704977 522 295023 7 54 655556 415 950266 107 705290 522 294710 6 55 655805 4:5 950202 107 705603 521 294397 5 56 656054 414 950138 107 705916 521 294084 4 57 656302 414 950074 107 706228 521 293772 3 58 656551 414 950010 107 706541 521 293459 2 59 656799 413 949945 107 706854 521 293146 1 60^ 6570471 413 949881 107 707166 520 292834 ' Cr^dne Sine 1 j Ootang. Tang. 1 M. J 63 Degrees. SINES AKD TANGENTS. (27 Degrees.) 45 M Bi.. D. Cosine | D. Tang. D. 1 Cotang. 9.657047 413 9.949881 107 9.707166 520 10.292834 60 1 657295 413 949816 107 707478 520 292522 59 3 657542 412 949752 107 707790 520 292210 58 3 657790 412 949688 108 708102 520 291898 57 4 658037 412 949623 108 708414 519 291586 56 6 658284 412 949558 108 708726 519 291274 55 6 658531 411 949494 108 709037 519 290963 54 7 658778 411 949429 108 709349 519 290651 53 8 669025 411 949364 108 709660 519 290340 52 9 659271 410 949300 108 709971 518 290029 51 10 11 659517 410 949235 108 108 710282 518 289718 50 49 9.659763 410 9.94^170 9^105 9.710593 518 10.289407 12 660009 409 108 710904 518 289096 48 13 660255 409 949040 108 711215 518 288785 47 14 660501 409 948975 108 711.525 517 288475 46 15 660746 409 948910 108 711836 517 288164 45 16 660991 408 948845 108 712146 517 287854 44 17 661236 408 948780 109 712456 517 287544 43 18 661481 408 948715 109 712766 516 287234 42 19 661726 407 948650 109 713076 516 286924 41 20 21 661970 407 948584 109 109 713386 516 286614 40 39 9.662214 407 9.948519 9.713696 516 10.286304 22 662459 407 948454 109 714005 516 285995 38 23 662703 406 948388 109 714314 515 285686 37 24 662946 406 948323 109 714624 515 285376 36 25 663190 406 948257 109 714933 515 285067 35 26 663433 405 948192 109 715242 515 284758 34 27 663677 405 948126 109 715551 514 284449 33 28 663920 405 948060 109 715860 514 284140 32 29 664163 405 947995 110 716168 514 283832 31 30 31 664406 404 404 947929 110 110 716477 9.716785 514 283523 30 29 9.664648 9.947863 514 10.283215 32 664891 404 947797 110 717093 513 282907 28 33 665133 403 947731 110 717401 513 282599 27 34 665375 403 947665 110 717709 513 282291 26 35 665617 403 947600 110 718017 513 281983 25 36 665859 402 947533 110 718325 513 281675 24 37 666100 402 947467 110 718633 512 281367 23 38 666342 402 947401 110 718940 512 281060 22 39 666583 402 947335 110 719248 512 280752 21 40 41 666824 401 947269 110 110 719555 9.719862 512 280445 20 19 9.667065 401 9.947203 512 10.280138 42 667305 401 947136 111 720169 511 279831 18 43 667546 401 947070 111 720476 511 279524 17 44 66778)5 400 947004 111 720783 511 279217 16 45 668027 400 946937 111 721089 511 278911 15 46 668267 400 946871 111 721396 511 278604 14 47 668506 399 946804 111 721702 510 278298 13 48 668746 399 946738 111 722009 ■ 510 277991 12 49 668986 399 946671 111 722315 510 277685 11 50 51 669225 399 946604 W. 722621 510 277379 10 9 9.669464 398 9,946538 9.722927 510 10.277073 52 669703 398 946471 Ill 723232 509 276768 8 53 669942 398 946404 111 723538 509 276462 7 54 670181 397 946337 111 723844 509 276156 6 55 670419 397 946270 112 724149 .509 275851 5 56 670658 397 946203 112 724454 509 275546 4 57 670896 397 946136 112 724759 508 275241 3 58 671134 396 946069 112 725065 508 274935 2 59 671372 396 946002 112 725369 508 274631 1 60 671609 396 945935 112 725674 508 274326 ;j Cosine Sine 1 1 Cotang. 1 Tang. jM.l 62 D^ees. 46 (28 Degrees.) a table or logarith3iic M 1 Siie 1 D. 1 Cosino 1 D. 1 Tans. ! -"■ f Co;ai;g. 1 ~o 9.671609 396 9.945935 lis . 9.725674 508 10.274326160 1 671847 395 945868 115 72597S 508 274021159 2 672084 395 945800 112 726284 507 2737161 58 3 67232] 395 945733 112 726588 507 273412 57 4 67255^ 395 945666 112 726892 507 273108! 56 5 67279£ 394 945598 112 727197 507 2728031 55 6 673032 394 945531 112 727501 507 2724991 54 7 673268 394 945464 113 727805 506 272195' 53 8 67350a 394 945396 113 728109 506 2718911 52 9 673741 393 945328 113 728412 506 271588151 10 11 673977 9.674213 393 945261 9.945193 113 113 728716 506 271284 50 393 9.729020 729323 506 10.270980 ,49 12 674448 392 945125 113 505 270677 148 13 674684 392 945058 113 729626 505 270374 47 14 674919 392 944990 113 729929 505 270071 46 15 675155 392 944922 113 730233 605 269767 45 26 17 18 675390 391 944854 113 730535 505 269465 44 675624 391 944786 113 730838 504 269162 43 675859 391 944718 113 731141 504 268859 42 19 676094 391 944650 113 731444 504 268556 41 20 21 676328 390 944582 114 114 731746 504 268254 10.267952 40 39 9.676562 390 9.944514 9.732048 504 22 676796 390 944446 114 732351 503 267649 38 23 677030 390 944377 114 732653 503 267347 37 24 677264 389 944309 114 732955 503 267045 36 25 677498 389 944241 114 733257 503 266743 35 26 677731 389 944172 114 733558 503 266442 34 27 677964 388 944104 114 733860 502 266140 33 28 678197 388 944036 114 734162 502 265838 32 29 678430 388 943967 114 734463 502 265537 31 30 31 678663 388 943899 9 . 943830 114 114 734764 502 265236 30 29 9 678895 387 9.735066 502 10.264934 32 679128 387 943761 114 ■ 735367 502 264633 28 33 679360 387 943693 115 735868 501 264332 27 34 679592 387 943624 115 735969 501 264031 26 35 679824 386 943555 115 736269 501 263731 25 36 680056 386 943486 115 736570 501 263430 24 37 680288 386 943417 115 736871 501 263129 23 38 680519 385 943348 115 737171 500 262829 22 39 680750 385 943279 115 737471 500 262529 21 40 41 680982 9.681213 385 943210 115 115 73V VVl 9.738071 500 262229 20 19 385 9.943141 500 10.261929 42 681443 384 943072 115 738371 500 261629 18 43 681674 384 943003 115 738671 499 261329 17 44 681905 384 942934 115 738971 499 261029 16 45 682135 384 942864 115 739271 499 260729 15 46 682365 383 942795 116 739570 499 260430 14 47 682595 383 942726 116 739870 499 260130 13 48 682825 383 942656 116 740169 499 259831 12 49 683055 383 942587 116 740468 498 259532 11 50 51 683284 9.683514 382 942517 116 116 740767 498 259233 10 9 382 9.942448 9.741066 498 10.258934 o2 683743 382 942378 116 741365 498 258635 8 53 683972 382 942308 116 741664 498 258336 7 54 684201 381 942239 116 741962 497 258038 6 55 684430 381 942169 116 742261 497 257739 5 56 684658 381 942099 116 742559 497 257441 4 57 684887 380 942029 116 742858 497 257142 3 58 685115 380 941959 116 743156 497 256844 2 59 685343 380 941889 117 743454 497 256546 1 60 685571 380 941819 117 743752 496 256248 1 Cosine ._.... . Sine 1 Cotang. 1 Taiig. 1 M. 1 61 Degr 3.es. SINES AND TANGENTS. (29 Degrees.) 47 M. 1 Sine D. 1 Cosine | D. Tang. 1 D. 1 Cotang. 1 9.685571 380 9.941819 117 9.743752 496 10.266248 60 1 685799 379 941749 117 744050 496 256950 59 2 686027 379 941679 117 744348 496 255662 58 3 686254 379 941609 117 744645 496 255365 57 4 686482 379 941539 117 744943 496 265067 66 5 686709 378 941469 117 745240 496 254760 55 6 686936 378 941398 117 745538 495 254462 54 7 687163 378 941328 117 745835 495 254165 53 8 687389 378 941258 117 746132 495 253868 52 9 687616 377 941187 117 746429 496 253671 51 10 11 687843 9.688069 377 941117 9.941046 117 118 746726 495 253274 60 49 377 9.747023 494 10.252977 12 688295 377 940975 118 747319 494 262681 48 13 688521 376 940905 118 747616 494 252384 47 14 688747 376 940834 118 747913 494 262087 46 15 688972 376 940763 118 748209 494 251791 46 16 689198 376 940693 118 748505 493 251495 44 17 689423 375 940622 118 748801 493 251199 43 18 689648 375 940551 118 T49097 493 250903 42 19 689873 375 940480 118 749393 493 260607 41 20 21 690098 375 940409 9.940338 118 118 749689 493 250311 40 39 9.690323 374 9.749985 493 10.250015 22 690548 374 940267 118 750281 492 249719 38 23 690772 374 940196 118 750576 492 249424 37 24 690996 374 940126 119 750872 492 249128 36 25 691220 373 940054 119 751167 492 248833 35 26 691444 373 939982 119 751462 492 248638 34 27 691668 373 939911 119 751757 492 248243 33 28 691892 373 939840 119 752052 491 247948 32 29 692115 372 939768 119 752347 491 247653 31 30 31 692339 372 939697 9.939625 119 119 752642 491 247358 930 9.692562 372 9.752937 491 10.247063 29 32 692785 371 939554 119 753231 491 246769 28 33 693008 371 939482 119 753526 491 246474 27 34 693231 371 939410 119 753820 490 246180 26 35 693453 371 939339 119 754115 490 245885 25 36 693676 370 939267 120 754409 490 245591 24 37 693898 370 939196 120 754703 490 245297 23 38 694120 370 939123 120 754997 490 245003 22 39 694342 370 939052 120 755291 490 244709 21 40 41 694564 9.694786 369 369 938980 9.938908 120 120 755685 489 244416 20 19 9.755878 489 10.244122 42 695007 369 938836 120 766172 489 243828 18 43 695229 369 938763 120 756465 489 243535 17 44 695450 368 938691 120 756759 489 243241 16 45 695671 368 938619 120 757052 489 242948 16 46 695892 368 938547 120 757345 488 242655 14 47 696113 368 938475 120 757638 488 242362 13 48 696334 367 938402 121 757931 488 242069 12 49 696554 367 938330 121 758224 488 241776 11 50 51 696775 367 938258 9.938185 121 121 758517 488 241483 10 9 9.696995 367 9.758810 488 10.241190 52 697215 366 938113 121 759102 487 240898 8 53 697435 366 938040 121 759395 487 240605 7 54 697654 366 937967 121 769687 487 240313 6 55 697874 366 937895 121 759979 487 240021 5 66 698094 365 937822 121 760272 487 239728 4 57 698313 365 937749 121 760564 487 239436 3 58 698532 365 937676 121 760866 486 239144 2 59 698751 365 937604 121 761148 486 238852 1 60 - 698970 364 937531 121 761439 486 238561 1 Cosine 1 Sine 1 1 Cotang. 1 1 Tang. 1 M. | 60 Desrees. 48 (30 Degrees.) a TABLE OF LOGARITHsnC Ti Sine 1 D. 1 Cosine | D. | Tang. 1 D. 1 Cotang. 1 1 9.698970 364 9.937531 121 9.761439 486 10.238561 60 1 699189 364 937458 122 761731 486 238269 59 2 699407 364 937385 122 762023 486 237977 58 3 699626 364 937312 122 762314 486 237686 57 4 699844 363 937238 122 762606 485 237394 56 5 700062 363 937165 122 762897 485 237103 55 6 700380 363 937092 122 763188 485 236812 54 7 700498 363 937019 122 763479 485 236521 53 8 700716 363 936946 122 763770 485 238230 52 9 700933 362 93^872 122 764061 485 235939 51 10 11 701151 9.701368 362 362 936799 9.936725 122 122 764352 484 235648 50 49 9.764643 484 10.235357 12 701585 362 936652 123 764933 484 235067 48 13 701802 361 936578 123 765224 484 234776 47 14 702019 361 936505 123 765514 484 234486 46 15 702236 361 936431 123 765805 484 234195 45 16 702452 361 936357 123 766095 484 233906 44 17 702669 360 936284 123 766385 483 233615 43 18 702885 360 936210 123 766675 483 233325 42 19 703101 360 936136 123 766965 483 233035 41 20 21 703317 360 936062 9.935988 123 123 767255 483 232745 40 39 9.703533 359 9.767545 483 10.232455 22 703749 359 935914 123 767834 483 232166 38 23 703964 359 935840 123 768124 482 231876 37 24 704179 359 935766 124 768413 482 231587 36 25 704395 359 935692 124 768703 482 231297 35 26 704610 358 935618 124 768992 482 231008 34 27 704825 358 935543 124 769281 482 230719 33 28 705040 358 935469 124 769570 482 230430 32 29 705254 358 935395 124 769860 481 230140 31 30 31 705469 357 935320 124 124 770148 9.770437 481 229852 30 29 9.705683 357 9.935246 481 10.229563 32 705898 357 935171 124 770726 481 229274 28 33 706112 357 935097 124 771015 481 228985 27 34 706326 356 935022 124 771303 481 228697 26 35 706539 356 934948 124 771592 481 228408 25 36 706753 356 934873 124 771880 4.80 228120 24 37 706967 356 934798 125 772168 480 227832 23 38 707180 355 934723 125 772457 480 227543 22 39 707393 355 934649 125 772745 480 227255 21 40 41 707606 355 934574 9.934499 125 125 773033 480 226967 20 19 9.707819 355 9.773.321 480 10.226679 42 708032 354 934424 125 773608 479 226392 18 43 708245 354 934349 125 773896 479 226104 17 44 708458 354 934274 125 774184 479 225816 16 45 , 708670 354 934199 125 774471 479 225529 15 46 708882 353 934123 125 774759 479 225241 14 47 709094 353 934048 125 775046 479 224954 13 48 709306 353 933973 125 775333 479 224667 12 49 709518 353 933898 126 775621 478 224379 11 50 51 709730 353 933822 9.933747 126 126 775908 478 224092 10 9 9.709941 352 9.776195 478 10.223805 52 710153 352 933671 126 776482 478 223518 8 53 710364 352 933596 126 776769 478 223231 7 54 710575 352 933520 126 777055 478 222945 6 55 710786 351 933445 126 777342 478 222658 5 56 710997 351 933369 126 .. 777628 477 222372 4 57 711208 351 933293 126 777915 477 222085 3 58 711419 351 933217 126 778201 477 221799 3 59 711629 350 933141 126 778487 477 221512 1 60 711839 350 933066 126 778774 477 221226 j Cosine i 1 Sine 1 j Cotang. 1 1 Tiy,g. I M. 1 59 Degrees. SINES A^'D TAKGErs-rs. (ol Degrees ) 49 M.l Sine T'. 1 losine { D. | Tati:. 1 D. Cotang. 1 9.711839 350 9.933066 126 9.778774 477 10.221226 60 1 712050 350 932990 127 779060 477 220940 59 2 712260 350 932914 127 779346 t76 220654 58 3 712469 349 i 932838 127 779632 476 220368 57 4 712679 349 i 932762 127 779918! 476 220082 56 5 712889 349 1 932685 127 7802031 476 219797 55 6 713098 349 1 932609 127 780489i 476 219511 54 7 713308 349 932533 J 27 780775 476 219225 53 8 713517 348 932457 127 781060 476 218940 52 9 713726 348 932380 127 781346 475 218654 51 10 IT 713935 9.714144 348 i 932304 ]27 127 7816311 9.781916; 475 475 218369 50 49 ^ 348 1 9.932228 10.218084 12 714352 347 932151 127 782201 475 217799 48 13 714561 347 i 932075 128 782486^ 475 217514 47 14 714769 347 931998 123 782771 475 217229 46 15 714978 347 931921 128 783056 475 216944 45 16 715186 347 931845 128 783341 475, 216659 44 17 71.5394 346 931768 128 783626 474i r 216374 43 18 715602 346 931691 128 783910 474 216090 42 19 715809 346 931614 123 784195 474 215805 41 20 21 716017 346 931537 9.931460 128 128 784479 474 215521 40 39 9.716224 345 9 . 784764 474 10.21.5236 22 716432 345 931383 128 785048 474 214952 38 23 716639 345 931306 128 785332 473 214668 37 24 716646 345 931229 129 785616 473 214384 36 25 717053 345 931152 129 785900 473 214100 35 26 717259 344 931075 129 786184 473 213816 34 27 717466 344 930998 129 786468 473 213.532 33 28 717673 344 930921 129 7867.52 473 213248 32- 29 717879 344 930843 129 787036 473 212964 31 30 31 718085 343 930766 129 129 787319 9.787603 472 472 212681 30 29 9.718291 343 9.930688 10.212397 32 718497 343 930611 129 787886 472 212114 28 33 718703 343 930533 129 788170 472 211830 27 34 718909 343 930456 129 788453 472 211547 26 35 719114 342 930378 1.29 788736 472 211264 25 36 719320 342 930300 130 789019 472 210981 24 37 719525 342 930223 130 789302 471 210698 23 38 719730 342 930145 130 789585 471 210415 22 39 719935 341 930067 130 789868 471 210132 21 40 41 720140 9.720.345 341 929989 9.929911 130 130 790151 471 209849 20 19 341 9.790433 471 10.209567 42 720549 341 929833 130 790716 471 209284 18 43 7207.54 340 929755 130 790999 471 209001 17 44 720958 340 929877 130 791281 471 208719 16 45 721162 340 929599 130 791563 470 208437 15 46 721366 340 929521 130 791846 470 208154 14 47 721570 340 929442 130 792128 470 207872 13 48 721774 339 929364 131 792410 470 207590 12 49 721978 339 929286 131 792692 1 470 207308 11 50 51 722181 339 92920? ]31 131 792974 i 470 207026 10 9 9 . 722385 339 9.929129 9.793256 : 470 10.206744 52 722588 339 929050 131 793538 i 469 206462 8 53 722791 338 928972 131 793819 1 469 206181 7 54 722994 338 928893 131 794101 469 205899 6 55 723197 338 928815 131 794383 j 469 205617 5 56 723400 338 928736 131 794664 ! 469 205336 4 57 723603 337 928657 131 794945 i 469 205055 3 58 723805 337 928578 131 795227 469 204773 2 59 724007 337 928499 131 795508 ! 468 204492 1 60 724210 337 928420 131 795789 1 468 204211 Cosine 1 1 Sine 1 1 Cotang. 1 1 Tang. |M.| 58 Degrees. G 50 (32 Degrees.) a table of logakithmic ^ 1 Sine 1 i>. 1 <:;nsi:!- 1 I> 1 T.u^. 1 D. 1 Cotang. 1 9,'7M-ZiU 33 r 9.9284^0 i:>'^ t>.7957Sb 468 10.204211 60 1 724412 337 92834^ 132 79607r 468 203930 59 2 724614 33(3 928263 132 796351 468 203649 58 3 724816 33-:^ 928183 132 79663? 4GS 203368 57 4 725017 336 928104 132 7969 i.S 468 20.3087 56 5 725219 336 928025 132 797194 468 202806 55 6 725420 335 927945 132 797475 468 202525 54 7 725622 335 i 9278G7 1S2 797755 468 202245 53 8 725823 335 9277 S7 132 79S036 467 201964 52 9 726024 335 92770S 132 798316 467 201684 51 10 11 726225 335 927629 132 132 793596 9 . 798877 467 301404 10.201123 50 49 9.726426 334 9.927549 467 12 726626 334 927470 133 799157 467 200843 48 13 726827 334 927390 133 799437 467 200563 47 14 727027 334 927310 133 799717 467 200283 46 15 727228 334 927231 133 799997 466 200003 45 16 72742t #333 927] 51 133 800277 466 1P9'723 44 17 727628 333 927071 133 800557 466 199443 43 18 727828 333 926991 133 800836 466 199164 42 19 728027 333 926911 133 801116 466 ^.98884 41 30 21 728227 9.728427 333 926831 9.926751 133 183 801396 466 198604 10.198325 40 39 332 9.801675 466 22 728^26 332 926671 133 601955 466 198046 38 23 728825 332 926591 133 802234 465 197766 37 24 729024 332 9';: 65 11 134 803513 465 197487 36 25 729223 331 926431 134 802792 465 197208 35 26 729422 331 9S6351 134 803072 465 196928 34 27 729621 331 92G270 134 803351 465 196649 33 28 729820 331 926190 134 803630 465 196370 32 29 730018 330 928110 134 803908 465 196092 31 30 31 730216 330 928029 9.925949 134 134 804187 465 195813 10.195534 30 29 9.730415 330 9.804486 464 32 730613 330 925868 134 804745 464 196255 38 33 730811 330 925788 134 805023 464 194977 37 34 731009 329 925707 134 805302 464 194698 36 35 731208 339 925626 134 805580 464 194420 35 36 731404 329 925545 135 805859 464 194141 24 37 731602 329 925465 135 806137 464 1933 63 S3 38 731799 329 925384 135 806415 463 193585 22 39 731996 328 925303 135 806693 463 193307 21 40 41 732193 328 925222 135 135 806971 463 193029 10.192751 20 19 9.732390 328 9.925141 9.807249 463 42 732.587 338 925060 135 807527 463 192473 18 43 732784 328 924979 135 807805 463 192195 17 44 732980 327 924897 1.35 808083 463 191917 16 45 733177 327 924S16 135 808361 463 191639 15 46 733373 327 924735 136 808638 462 191362 14 47 733569 327 924854 136 808916 462 191084 13 48 733765 327 924572 136 809193 462 190807 12 49 733961 326 924491 136i 809471 462 190529 11 50 51 734157 326 924409 9.924328 136 136 809748 9.810025 462 190262 10.189975 10 "9 9.734353 326 463 52 734549 326 924246 136 810302 462 189698 8 53 734744 325 924164 lo'6 810580 462 189420 7 54 734939 325 - 924083 136 810857! 462 189143 6 55 .735135 325 924001 136 811134 461 188866 5 56 735330 325 923919 136 811410 461 188590 4 67 735525 325 923837 136 811687 461 188313 3 58 735719 324 923755 137 811964 461 188036 2 59 735914 324 923673 137 812241 461 187759 1 60 736109 324 1 9235911 137 81 ^n?^ A81 187483 S ' t Cosine j 1 &uie 1 1 Cotang. 1 Tang. |M.j SINES AND TANGENTS . (33 D egrees ■) 51 _mJ Sine 1 D. Cusii!^ 1 D. T,Ml,g. 1 D. ■ <:oi.anr. ! 9.736109 324 9.923591 137 9.812517 461 10.187483 60 1 736303 324 923509 137 812794 461 187206 59 2 736498 324 923427 137 813070 461 186930 58 3 736692 323 923345 137 813347 460 186653 57 4 736886 323 9232G3 137 813623 460 186.377 56 5 737080 323 923181 137 813899 460 186101 55 6 737274 323 923098 137 814175 400 185825 54 7 737467 323 923016 137 814452 460 185548 53 8 737661 322 922933 137 814728 460 18.5272 52 9 737855 322 922851 137 815004 460 184996 51 10 11 738048 9.738241 322 322 922788 9.922686 138 138 815279 460 184721 50 49 9,815555 459 10.184445 12 738434 322 922603 138 815831 459 184169 48 13 738627 321 922530 138 816107 459 183893 47 14 738820 321 92243S 138 816382 459 183618 46 15 739013 321 922355 138 816658 459 183342 45 16 739206 321 922272 138 816933 459 183067 44 17 739398 321 922189 138 817209 459 182791 43 18 739590 320 922106 138 817484 459 182516 42 19 739783 320 922023 138 81 7759 459 182241 41 20 21 739975 320 921940 9.921857 138 139 818035 458 181965 10.181690 40 39 9.740167 320 9.818310 458 22 740359 320 921774 139 818585 458 181415 38 23 740550 319 921691 139 818860 458 181140 37 24 7407^3 319 921607 139 819135 458 180865 36 25 740934 319 921524 139 819410 458 180590 35 26 741125 319 921441 139 819684 458 180316 34 27 741316 319 921357 139 819959 458 180041 33 2S 741508 318 921274 139 820234 458 179766 32 29 741699 318 921190 139 820508 457 179492 31 30 31 741S89 9.742080 318 921107 9.921023 139 139 820783 457 179217 30 29 318 9.821057 457 10.178943 32 742271 318 920939 140 821332 457 178668 28 33 742462 317 920856 140 821606 457 178394 2? 34 742652 317 920772 140 821880 457 178120 26 35 742842 317 920688 140 822154 457 177846 25 36 743033 317 920604 140 822429 457 177571 24 37 743223 317 920520 140 822703 457 177297 23 3S 743413 316 920436 140 822977 456 177023 22 39 743602 318 920352 140 823250 456 176750 21 40 743792 316 920268 140 823524 456 176476 20 41 9.743982 316 9.920184 140 9.823798 456 10.176202 19 42 744171 316 920099 140 824072 456 175928 18 43 744361 315 920015 140 824345 456 175655 17 44 744550 315 919931 141 824619 456 175381 16 45 744739 315 919846 141 824893 456 175107 15 46 744928 315 919762 141 825166 456 174834 14 47 745117 315 919677 141 825439 455 174561 13 48 745306 314 919593 141 825713 455 174287 12 49 745494 314 919508 141 825986 455 174014 11 50 745G83 314 1 919424 141 826259 455 173741 10 51 9.745871 314 19.919339 141 9.826532 455 10.173468 9 53 74G059 314 1 919254 141 826805 455 173195 8 53 746248 313 919169 141 827078 455 172922 7 54 746436 313 919035 141 827351 455 172649 6 55 746624 313 919000 141 827624 455 172376 5 56 746812 813 918915 142 827897 454 172103 4 57 746999 313 91SS30 142 828170 4.54 171830 3 58 747187 .312 918745 142 828442 454 I7I558 2 69 747374 312 918659 142 828715 454 171285 1 60 747562 312 918574 142 828987 454 171013 Cosine j-..^'"^ 1 Cotang. k^ 1 Tang. 1 M. 56 D*- ^•^t: 52 '34 Decrrees. ; a table of LOGAEirn^ac .'i. Sine D. • .^:.:- Il Ta.?. Tl. (_••■'• J. 9.747562 3i2 9.yi!'o7-i 142 i).^2^y'-7 454 iU.i7l!lti3 »^M 1 747749 312 918489 142 829260 454 17074'.i 59 2 1 747936 312 918404: 142 829532 454 170468 5S 3 748123 311 91831 S' 142 829S05 454 170195 57 i 74*31U 311 9iS233i 142 830077 454 169923 56 5 748497 311 9iSl47 142 830349 453 169651 55 6 748683 311 9ISU62; 142 8:30621 453 169379 .54 7 748S70 311 9179 76 143 830893 453 169107 .53 8 749056 310 917891> 143 831165 453 168835 52 9 749243 310 917805 143 8314:37 453 16S563 5; 10 749429 310 917719= 143 831709 453 iaS291 5i» 11 9.749515 310 9.9176:34 143 9. 831951 453 10.168019 49 13 749801 310 917548 143 832253 453 167747 48 13 749987 309 917462: 143 832525 453 167475 47 14 750172 309 917376 143 8:32796 453 167-^04 46 15 75035 S 309 917290 143 8:33n6S- 452 166932 45 16 750543 309 917204 143 V 3 3 :-■ - :. 452 166661 44 17 750729 309 917118 14i -■:•?: 11 452 166:3S9 4:3 18 750914 308 917032 14^ - 3 3 *■" "^ 452 1661 IS 42 19 751099 30S 916940 :.. S341.54 452 165S46 4i 20 21 7512>4 9.751469 30 S 30S 9i6«'5- .^^ 9.916773 144 S3 442 5 452 165575 40 10.165:304 39 9.5;34696- 452 23 751654 308 9166S7 144 834967 4.52 1650:33 35 23 751839 308 916600 144 8:3523§ 452 164762 37 24 752023 307 916514 1^4 -35509 452 164491 36 25 75220 S 307 91fr42T :« -35780 451 164220 35 26 752392 307 916341 144 >36051 451 16:3949 34 27 752576 307 916254 144 836322 451 16:367- :33 28 752760 307 916167 145 836593 451 16:34^7^ 32 29 752944 306 9160S1. 145 836S64 451 163136 31 30 753 12s 306 915994 145 8371:34 451 162866 :30 31 9.753312 3l»d 9.915907 145 9.8:37405 451 10.162595 29 32 753495 306 915520 145 837675 451 162325 25 33 753679 306 9157:33 14.5 837946 451 162054 27 34 753S62 305 915646 14-5 S3S216 451 16 1754 2o 35 7M046 305 915559 145 83S4S7 450 161513 25 36 754229 305 915472 145 ?3-7o7 450 161243 24 37 754412 305 9153S5 145 ^d':>('-2~ 450 160973 23 38 754.595 305 915297 145 ^S'-^'Z^T 4.50 160703 22 39 75477 S 304 915210 145 S3y5nH 450 1604:32 21 40 41 754960 9.75514:3 304 304 915123 146 9.915035 14^ 83yS3S 9.S4':iins 450 450 160162 20 10.159592 19 42 75.5326 304 91494- :-- ?-v3^- 450 159622 IS 43 75550S 304 914S-3V ,- 't^ ^ .: ' 450 1593.53 17 44 755690 304 914773 1^6 ■^ ^^' - 1 7 449 159053 16 45 755872 303 9146S5 146 ^-il 1^7 449 155813 15 46 7560.54 303 914598- 146 S41^.5: 449 15554:3 14 47 756236 303 914510 146 841726 449 155274 13 48 75641 S 3U3 914422 146 841996 449 1.58004 12 49 756600 303 9143:W 146 842266 449 157734 11 50 756782 302 914246 147 842535 449 157465 10 51 9.756963 302 9.91415S 147 9.842S05 449 10.157195' 9 52 757144 .302 914070 147 843074 449 156926: 8 53 757326 302 9139S2 147 843:34:3 449 156657 7 54 757507 302 913S94 147 84:3612 449 156:385: 6 55 757688 301 ■ 913S06 147 843SS2 448 156118' 5 56 7.57869 301 913718 147 844151 44S 15.5549. 4 57' 758050 301 913630 147. 844420 44S 155580. 3 68 758230. 301 913541. 147^ 8446 S 9 44S I55311i 2 59 758411:' 301 ' 913453 147j 84495 ?t 44S 155042 1 60 75*591 301 I 913365 147 845227 448 1.54773. i Cx-:ne Siiie Ciaaz Tang. , -M. SINES AND TANGENTS . (33 Degrees. ) 63 xM. 1 Sine D. Cosine 1 D. Tansr. 1 r.. 1 Cota... 1 1 "T 9.753591 301 9.913365 147 9.845227 448 10.154773 60 I 758772 300 913276 147 84.5496 448 154504 59 o 758952 300 913187 148 845764 448 154236 58 3 759132 300 913099 148 846033 448 153967 57 4 759312 300 913010 148 846302 448 153698 56 5 759492 300 912922 148 846570 447 153430 55 6 759672 299 912833 148 846839 447 153161 54 7 769852 299 912744 148 847107 447 152893 53 8 760031 299 912655 148 847376 447 152624 52 9 760211 299 912566 148 847644 447 152366 51 10 11 760390 9.760569 299 912477 9.912388 148 148 847913 447 152087 50 49 298 9.84S181 447 10.151819 12 760748 298 912299 149 848449 447 151551 AS 13 760927 298 912210 149 848717 447 151283 47 14 761106 298 912121 149 818986 447 151014 46 15 761285 298 912031 149 849254 447 150746 45 16 761464 298 911942 149 849522 447 150478 44 17 761642 297 911853 149 849790 446 150210 43 18 761821 297 911763 149 850058 446 149942 42 19 761999 297 911674 149 850325 446 149675 41 20 21 762177 297 911584 9.911495 149 149 850593 446 149407 10.149139 40 39 9.762356 297 9.850861 446 22 762534 296 911405 149 851129 446 148871 38 23 762712 296 911315 150 851396 446 148604 37 24 762889 296 911226 150 851664 446 148336 36 25 763067 296 911136 150 851931 446 148069 35 26 763245 296 911046 150 852199 '146 147801 34 27 763422 296 910956 150 852466 446 147534 33 28 763600 295 910S66 150 852733 445 147267 32 29 763777 295 910776 150 853001 445 146999 31 30 31 763954 295 910686 150 150 853268 445 146732 30 29 9.764131 295 9.910596 9.853535 445 10.146465 32 764308 295 91 0500 150 853802 445 146198 28 33 764485 294 910415 1.50 854069 445 145931 27 34 764662 294 910325 151 854336 445 145864 26 35 764838 294 910235 151 854603 445 145397 25 36 765015 294 910144 151 854870 445 145130 24 37 765191 294 910054 151 855137 445 144863 23 38 765367 294 909963 151 855404 445 144596 22 39 765544 293 909873 151 855671 444 144329 21 40 41 765720 293 909782 9. 90969 J 151 151 85593S 444 144062 I0.14379li 20 19 9.765896 293 9.856204 444 42 766072 293 90960. 151 856471 444 143529 18 43 766247 293 009510 151 856737 444 143203 17 44 766423 293 909419 151 857004 444 142996 16 45 766598 292 909328 152 857270 444 142730 15 46 766774 292 909237 152 857537 444 142463 14 47 766949 292 909146 152 857802 868069 444 142 197 13 48 ■ 767124 292 909055 152 444 141931 12 49 767300 292 908964 152 868336 444 141664 11 50 51 767475 291 908873 9.908781 152 152 858602 443 141398 10.141132 10 9 9.767649 291 9 . 868868 443 52 767824 291 908690 152 8591.34 443 140866 8 53 767999 291 908599 152 859400 443 140600 7 54 768173 291 908507 152 859665 443 140334 6 55 768348 290 908416 153 859932 443 140068 c 56 768522 290 908324 153 860198 443 139802 4 57 768697 290 908233 153 860464 443 139536 3 58 768871 290 908141 153 860730 443 139270 2 59 769045 290 908049 153 860995 443 139005 1 60 769219 290 907958 153 861261 443 138739 r..-x^ 1 S.-.e 1 .>..„... 1 T:., . 1 M. 1 54 Decrees. 54 (36 Degrees.) a TABLE OF LOGARITHMIC Sin(> 1 B. 1 Cn.... 1 ,. <;ms. \ D. 1 Cotanu. 1 [. 9.769219 290 9.907958 153 9.861261 443 10.138739 60 1 769393 289 907866 163 861527 443 138473 59 2 769566 289 907774 153 861792 442 138208 58 3 769740 289 907682 153 862058 442 137942 57 4 769913 289 907590 153 892323 442 137677 56 6 7700S7 289 907498 153 8G2589 442 137411 55 6 770260 288 907406 153 862854 442 137146 54 7 770433 288 907314 154 863ii9 442 136881 53 8 770606 288 907222 164 863385 442 136615 62 9 770779 288 907129 154 863650 442 136350 51 10 11 770952 288 907037 9.906945 154 154 863915 442 136086 50 49 9.771125 288 9.864180 442 10.135820 12 771298 287 906852 154 864445 442 135555 48 13 771470 287 906760 154 864710 442 135290 47 14 771643 287 906667 154 864975 441 135025 46 15 771815 287 906575 154 8fi5240 441 134760 45 16 771987 287 906482 154 8G5505 441 134495 44 17 772159 287 906389 155 865770 441 134230 43 18 772331 286 906296 155 866035 441 133965 42 19 772503 286 906204 155 866300 441 133700 41 20 21 772675 286 906111 155 155 866564 9 7806829 441 133436 40 39 9.772847 286 9.906018 441 10.133171 22 773018 286 905925 155 867094 441 132906 38 23 773190 286 905832 155 867358 441 132642 37 24 773361 285 905739 155 867623 441 132377 36 25 773533 285 905645 155 867887 441 132113 35 26 773704 285 905552 155 868152 440 131848 34 27 773875 285 905469 155 868413 440 131584 33 28 774046 285 905366 156 868680 440 131320 32 29 774217 285 9>'5272 156 868945 440 131056 31 30 31 774388 284 284 9!»5i79 156 156 869209 9.869473 440 440 130791 10.130527 30 29 1 9.7745.58 9.905085 32 774729 284 904992 156 869737 440 130263 28 33 774899 284 904898 156 870001 440 129999 27 34 775070 284 904804 156 870265 440 l297^^5 26 35 775240 284 904711 156 870529 440 12947 i 25 36 775410 283 904617 156 870793 440 129207 24 37 775580 283 904523 156 871067 440 128943 23 38 775750 283 904429 157 871321 440 128679 22 39 775920 283 904335 157 871585 440 128415 21 40 41 776090 283 904241 167 157 871849 9.872112 439 439 128161 10.127888 20 19 9.776259 283 9.904147 42 776429 282 904053 157 87':.3';6 439 127624 18 43 776598 282 903959 157 87:^640 439 127360 17 44 7767r.8 282 903864 157 87a903 439 127097 16 45 776937 282 903770 157 873167 439 126833 15 46 777106 282 903676 157 873430 439 126570 14 47 777275 281 ^903581 •903487 157 873694 439 126306 13 48 777444 281 157 873957 439 126043 12 49 777613 281 903392 158 874220 439 125780 11 50 51 777781 281 -903298 158 158 874484 439 12.5516 10 9 9.777950 281 9.903203 9.874747 439 110.125253 52 778119 281 903108 168 876010 439 124990 8 53 778287 280 903014 158 875273 438 124727 7 54 778455 280 902919 158 875536 438 124464 6 55 778624 280 902824 158 876800 438 124200 5 56 778792 280 902729 158 876063 438 123937 4 57 778961 280 902634 158 876326 438 123674 3 58 77912S 280 902539 159 876589 438 123411 2 59 77929f ) 279 902444 1.59 876851 438 123149 I 60 77946E 5 279 902349 i 159 877114 1 438 122886 1 Cosinft 1 1 Sine 1 1 Cotai.p. i I Ta.. 1 M 1 53 Degrees. SINES AND TANGENTS. (37 Degrees •) 65 M. Si. ,;. 1 a.sr,fi 1 D. T ; ■V r.i..,.. 1 1 "0" 9.779463 279 9.902349 159 9.877114 438 10.122886 60 1 • 779331 279 902253 159 87737 f 438 122623 59 2 779798 279 902158 159 877640 438 122360 58 3 779966 279 902033 159 877903 438 122097 57 4 780133 279 901967 159 878165 438 121835 56 5 780300 278 901872 159 878428 438 121.572 55 6 780467 278 901776 159 878691 438 121309 54 7 780634 278 901681 159 878953 437 121047 53 8 780801 278 9015S5 159 8792:6 437 120784 52 9 780968 278 901490 159 879478 437 120522 51 10 781134 278 901394 160 8/9741 437 120259 50 11 9.7S1301 277 9.901298 160 9.880003 437 10.119997 49 12 781468 277 901202 160 8^:)265 437 119735 48 13 781634 277 901106 160 S80528 437 119472 47 14 781800 277 901010 160 880790 437 119210 46 15 781966 277 900914 160 881052 437 118948 45 16 782.32 277 900818 160 881314 437 118686 44 '7 782298 276 900722 160 881576 437 118424 43 i8 7824:64 276 900626 160 88 1839 437 118161 42 l9 782630 276 900529 160 882101 437 117899 41 ■zo 782796 276 900433 161 8^23-^^3 436 117337 40 ■zl 9.782961 276 9.900337 161 9.882625 436 10.117375 39 22 783127 276 • 900240 161 83:8887 436 117113 38 23 7S3292 275 900144: 161 883148 436 116852 37 24 783453 2/5 90004/ 161 883410 436 116590 36 ■Zr> 783623 275 89995 i 161 883672 436 116328 35 26 7837S3 275 899854 161 883934 436 116066 34 27 783953 275 899757 161 8S4196 436 115804 33 28 784118 275 899660 161 884457 436 115543 32 29 7842S2 274 899564 161 884719 i36 115281 31 30 784447 274 899467 162 S84980 436 115020 30 31 9.784612 274 9.899370 162 Q.SSiyz'lz 436 10.114753 29 32 784776 274 899273 162 385503 436 114497 28 33 784941 274 899173 182 88 5765 436 114235 27 34 785105 274 899073 162 88 6026 436 113974 26 35 785269 273 898981 162 886288 436 113712 25 36 785433 273 898884 162 886549 435 113451 24 37 7S55)7 273 89S787 162 886810 435 113190 23 38 785761 273 898689 162 887072 435 112928 22 39 785925 273 898592 162 887333 435 112667 21 iO 41 7860S9 273 898494 9.898397 163 163 887594 9.887855 435 435 112406 20 19 9.786252 272 10.112145 42 786416 272 898299 163 888.16 435 111884 18 43 7865/9 272 898202 163 888377 435 111623 17 44 786742 272 898104 163 888639 435 111361 16 45 786906 272 898006 163 888900 435 111100 15 46 787069 272 897908 163 839160 435 110840 14 47 787232 271 897810 163 83942 [ 435 110579 13 48 787395 271 897712 163 889682 435 110318 12 49 787557 271 897614 163 839943 435 110057 11 50 51 787720 271 697516 9.897418 163 164 890204 434 109796 10 9 9.787883 27] 9.890465 434 10.109535 52 788045 271 897320 164 8907ai 434 109275 8 53 788208 271 897222 164 890986 434 109014 7 54 788370 270 897123 164 891247 434 108753 6 55 788532 270 897025 164 891.507 434 108493 5 56 788694 270 896926 164 891768 434 108232 4 57 788856 270 896828 164 892028 434 107972 3 58 789018 270 896729 164 892283 434 107711 2 59 789180 270 896631 164 892549 434 107451 1 60 789342 269 896532 164 892310 434 107190 ~\ ■..'..si..: Siae ! Oot ,g. Ta„g. 1 J 56 (38 Degrees.) a TABLE OF LOGARITHMIC ... 1 •>. , u.'.u. I D. ! T.- U. Cotany. 1 IT 9.789342 269 9.896532 134 9.892810 434 10. 107190; 60 1 789504 269 8964S3 165 893070 434 1069301 59 2 789665 269 896335 165 893331 434 106669 58 3 789827 239 896236 165 89.3591 434 106409 57 4 789988 269 896137 165 893851 434 106149 56 5 790149 269 896038 165 894111 434 105889 55 6 790310 268 895939 165 894371 434 105629 54 7 790471 268 895840 165 894632 433 10.5368 53 8 790632 268 895741 165 894892 433 105108 52 9 790793 268 895641 165 895152 433 104848 51 10 11 790954 268 895542 9. G 95443 165 166 895412 9.895672 433 104588 50 49 9.791115 268 433 10.104328 12 791275 267 895343 163 895932 433 104068 48 13 791436 267 895244 166 893192 433 103808 47 14 791596 267 895145 166 896452 433 103548 46 15 791757 267 89504?. 163 896712 433 103288 45 16 791917 267 894945 166 896971 433 103029 44 17 792077 267 894846 166 897231 433 102769 43 18 792237 266 894746 166 897491 433 102509 42 19 792397 266 894646 166 897751 433 102249 41 20 21 792557 9.792716 26. '^^ 894546 166 167 898010 433 101990 40 39 266 9.894446 9.898270 433 10.101730 22 792876 266 894346 167 89-530 433 101470 38 23 793035 266 894246 167 89S789 433 101211 37 24 793195 265 894146 167 899049 432 100951 36 25 793354 265 894046 187 899308 432 100692 35 23 793514 265 893946 167 899568 432 100432 34 27 793673 255 893846 167 839827 432 100173 33 2S 79S832 265 893745 167 900086 432 099914 32 29 7939yl 265 893i;.45 167 900.346 432 0996.54 31 30 31 794150 264 89334 4 9.893444 167 168 900605 432 039395 30 29 9.794J?0'N 26^ 9.900864 432 10.099136 32 794437 264 893343 168 901124 432 098376 28 33 794626 264 893243 168 90 ms" 432 098617 27 34 794784 264 893142 168 901642 432 098358 26 35 794942 264 893041 168 901901 432 098099 25 36 795101 264 892940 168 902160 432 097840 24 37 795259 263 892839 168 902419 432 ■ 097581 23 38 795417 263 892709 168 902679 432 097321 22 39 795o75 263 892638 168 902938 432 097062 21 40 795733 263 892536 168 903197 431 096803 20 41 9.795S91 263 9.892435 169 9.903455 ■ 431 10.096545 19 42 796049 263 892334 169 90.-^714 431 096286 18 43 796-206 263 892233 169 903973 431 096027 17 44 793364 262 892132 169 904232 431 095768 16 45 796521 262 89203;) 169 904491 431 095509 15 46 79667y 262 891920 169 904750 431 09.5250 14 47 796S36 262 891827 139 905008 431 094992 13 48 796993 262 891726 169 905267 431 094733 12 49 7971.50 261 891624 169 fj05526 431 094474 11 50 51 797307 9.797464 261 8915-J3 ^891421 ^89 13 i 9 170 170 905734 9.903043 431 431 094213 10 9 261 10.093957 52 7976.il 261 170 90-302 431 093898 8 53 7977-7 261 891217 170 903360 431 093440 7 54 797934 261 891115 170 906819 431 093 LSI 6 55 798091 281 891013 170 907077 431 092923 5 56 798247 261 890911 170 907336 431 092664 4 57 798403 260 890809 170 907594 431 092406 3 58 7985H0 260 890707 170 907852 431 092148 2 59 798716 260 890n05 170 908111 430 091889 1 60 798872 260 890503 170 90S369 430 091631 1 Cosine " Si.e 1 '^oiai: 1 -avg. 1 M I 51 Degrees. SINES AND TANGENTS. (39 Degrees.) 57 \i 1 ?.., 1 I' 1 <:•■ 1.* 1 >•. ! 'J'aiig. 1 D. 1 Coiaiig. 1 j "^ 9.79887ii 1 260 9.890503 170 9.908369 430 10.091631 60 1 799028 260 890400 171 908628 430 091372 59 2 799184 260 890298 171 908886 430 091114 58 3 799339 259 890195 171 909144 430 090856 57 4 799495 259 890093 171 909402 430 090598 56 5 799651 259 889990 171 909660 430 090340 55 6 799806 259 889888 171 909918 430 090082 54 7 799962 259 889785 171 910177 430 089823 53 8 800117 259 889682 171 910435 430 089565 52 9 , 800272 258 889579 171 910693 430 089307 51 10 11 800427 258 889477 171 172 910951 430 089049 50 49 9.800582 258 9.889374 9.911209 430 10.088791 12 800737 258 889271 172 911467 430 088533 48 13 800892 258 889168 172 911724 430 088276 47 14 801047 258 889064 172 911982 430 088018 46 15 801201 258 888961 172 912240 430 087760 45 16 801356 257 888858 172 912498 430 087502 44 17 801511 257 888765 172 912756 430 087244 43 18 801665 257 888651 172 913014 429 086986 42 19 801819 257 888548 172 913271 429 086729 41 20 21 801973 9.802128 257 257 888444 173 173 913529 429 086471 40 39 9.888341 9.913787 429 10.086213 22 802282 256 888237 173 914044 429 085956 38 23 802436 256 888134 173 914302 429 085698 37 24 802589 256 888030 173 914560 429 085440 36 25 802743 256 887926 173 914817 429 085183 35 26 802897 256 887822 173 915075 429 084925 34 27 803050 256 887718 173 915332 429 084668 33 28 803204 256 887614 173 915590 429 084410 32 29 803357 255 887510 173 915847 429 084153 31 30 31 803511 255 887406 9.887302 174 174 916104 429 083896 30 29 9.803664 255 9.916362 429 10.083638 32 803817 255 887198 174 916619 429 083381 28 33 803970 255 887093 174 916877 429 083123 27 34 804123 255 886989 174 917134 429 082866 26 35 804276 254 886885 174 91739] 429 082609 25 36 804428 254 886780 174 917648 429 082352 24 37 804581 254 886676 174 917905 429 082095 23 38 804734 254 886571 174 918163 428 081837 22 39 804886 254 886466 174 918420' 428 081580 21 40 41 805039 9.805191 254 886362 9.886257 175 175 918677' 428 081323 10.081066 20 19 254 9.918934 428 42 805343 253 886152 175 919191 428 080809 18 43 805495 253 886047 175 919448 428 080552 17 44 805647 253 885942 175 919705 428 080295 16 45 805799 253 885837 175 919962 428 • 080038 15 46 805951 253 885732 175 920219 428 079781 14 47 806103 253 885627 175 9204761 428 079524 13 48 806254 253 885522 175 920733, 428 079267 12 49 806406 252 885416 175 920990 428 079010 11 50 51 806557 9. 806709 i 806860 807011 252 885311 176 176 9212471 428 078753 10 9 252 9.885205 .9.921503 428 10.078497 52 252 885100 176 921760 428 078240 8 53 252 884994 176 922017' 428 077983 7 54 807163 252 884889 176 922274! 428 077726 6 55 807314 252 884783 176 9225301 428 077470 5 56 807465 251 884677 176 9227871 428 077213 4 57 807615 251 884572 176 9230441 428 07695G 3 58 807766 251 884466 176 923300 428 076700 2 59 807917 251 884360 176 923557 427 076443 1 60 808067 251 8842541 177t 923813 427 076187 Li Cosine 1 1 S.ne 1 1 Coianir. 1 1 Tang. j M. | 50 Degrees. H (40 Desrrces."^ a table or logabithiiic 9. SO' 067' 251 I 9 :S 251 250 ^ 250 - 250 250 250 250 1? -±y 50 51 dv. 53 5-± 55 56 57 14460 14607 14753 14900 1.5<:Mr6 15193 15339 15485 9.S15631 lo'-iO 16361 L6507 16652 16795 ■16345 ■ ? ' :-' -. 24fi _ .- , ■> y 246 ' ,--- "• 245 i.io. ? 245 13725 245 13S73 245 244 244 244 244 244 244 244 243 ' 24:3 243 •243 24:3 243 243 242 242 242 242 9.SHif^ i K _ ■ ^M ?> i . ^. — > ? ■; r •: : SSa^-iy 1 ( 7 8S3723 177 8S3517 " 77 ii:- ?':::_ "* ^ ■: , 7 - , - ^ .- '^- - --:— > ^ ', r . . >, S S '1 S " 1 '78' S ^ ■- ~ ' ^ ~>. 5 ^ , ; : " ~ ■: ^ ^ ', ' " ■ "^ SS'l'41r.: SS233-: ~ '- S?22i.r ^ "* 2 1 2 1 17 r -• . "^82014 17 r si" 'r>' ~ ssiT--:- 1"- ^ ^ ' - ^ -^ ■ ~ - vi - ---. S- „^^ t»3i.5oy 1 «>* 881261 180? «Sil53 ISO' ^^ .'}^: I-— ' 11 il' 'I - S * ; " "1 Q _^ . ii-.A - :- 8305V = 88039 »«0-2~r S 5 '} 1 ^ J ^ V 3^. ii '-..i---' " ^1 • ' - ' ; : ; :5i 1^1 ; 7 - 7^- S7yDb~ S7952.: _ ^ - 87&42U • X- 879311 -li.- 879202 18-; 879C»93 18': 87S9S4 18-: S78S75 !».•; Z. _ i.7i7nr; . 18C S7'i656 - i--- 875547 I'^C 87*4:^? 18-: S7S32^ I''- 87521 r " - - >» , ^ 1 ■ - 877&r: 8778- 87778: '.Q76187" 60 075930 59 075673 58 o7 427 427 427 437 9268^1 9271471 f*2^'^4'"»3' 281711 28427^ C-68t3' 427 427 427 427 427 427 427 427 427 427 427 ' 075417 075160 53 0749<:i4 55 074-648 54 074391 53 074135 52 073-78 51 073622 50 10.073366! 49 073110 48 072853 47 072597 46 072341 45 072«}S5 44 07 IS 29 43 071573 42 071317 41 071060 40 ^2 a 426 426 425 ae 10.070804 39 070548 3S 07CHi92 37 070036 35 069780 35 069525 34 069269j 33 069013 0687571 31 068501 9335451 933800^ ? 3-40 3 3 428 428 426 ^6 426 426 426 426 426 * ,3 .:33 426 426 426 426 426 32 30 29 10.068245 067990 067734i27 06717?' -28 0--2CC 25 uo6711 23 066455 066200 065944 20 10.065689 19 065433 13 065177 0649?2 16 13 Tali "MT s INES AND TAKGi :?,TS . (41 Degrees 59 M .in. 1 D. Cosiiie 1 D. D. Colang. 1 1 9.816943 242 9.877780 183 9.939163 425 10.060837 60 1 817088 242 877670 183 939418 425 060582 59 2 817233 242 877560 183 939673 425 060327 58 3 817379 242 877450 183 939928 425 060072 57 4 817524 241 877340 183 940183 425 059817 56 5 817668 241 877230 184 940438 425 059562 56 6 817813 241 877120 184 940694 425 0.59306 54 7 817958 241 877010 184 940949 425 059051 53 8 818103 241 876899 184 941204 425 058796 52 9 818247 241 876789 184 941458 425 058542 51 10 11 818392 241 876678 184 184 941714 425 058286 50 49 9.818536 240 9.876568 9.941968 425 10.058032 12 818681 240 876457 184 942223 425 057777 48 13 818825 240 876347 184 942478 425 057522 47 14 818969 240 876236 185 942733 426 057267 46 15 819113 240 876125 185 942988 425 057012 45 16 819257 240 876014 185 943243 425 056757 44 17 819401 240 875904 185 943498 426 056502 43 18 819545 239 875793 185 943752 425 056248 42 19^ 819689 239 875682 185 944007 426 05.5993 41 20 21 819832 239 875571 9.875459 185 185 944262 425 055738 40 39 9.819976 239 9.944517 425 10.055483 22 820120 239 875348 186 944771 424 055229 38 23 820263 239 875237 185 945026 424 054974 37 24 820406 239 875126 186 94.5281 424 054719 36 25 820550 238 875014 186 945535 424 054465 36 26 820693 238 874903 186 945790 424 054210 34 27 820836 238 874791 186 946045 424 053956 33 28 820979 238 874680 186 946299 424 053701 32 29 821122 238 874568 186 946554 424 053446 31 30 31 821265 238 874456 9.874344 186 186 946808 424 0.53192 30 29 9.821407 238 9.947063 424 10.052937 32 8215.50 238 874232 187 947318 424 0.52682 28 33 821693 237 874121 187 947572 424 052428 27 34 821835 237 874009 187 947826 424 062174 26 35 821977 237 873896 187 948081 424 051919 25 36 822120 237 873784 187 948336 424 051664 24 37 822262 237 873672 187 948590 424 051410 23 38 822404 237 873560 187 948844 424 061156 22 39 822546 237 873448 187 949099 424 050901 21 40 41 822688 9.822830 236 236 873335 9.873223 187 187 949353 424 050847 20 19 9.949607 424 10.060393 42 822972 2.36 873110 188 949862 424 0.50138 18 43 823114 236 872998 188 950116 424 049884 17 44 823255 236 872885 188 950370 424 049630 16 45 823397 236 872772 188 950625 424 049375 16 46 823539 236 872659 188 950879 424 049121 14 47 823680 235 872547 188 951133 424 048867 13 48 823821 235 872434 188 951388 424 048612 12 49 823963 235 872321 188 951642 424 048358 11 50 51 824104 235 872208 9.872095 188 189 951896 424 048104 10 9 9.824245 235 9.952150 424 10.047860 52 824386 235 871981 189 952405 424 047595 8 53 824527 235 871868 189 952659 424 047341 7 54 824668 234 871755 189 952913 424 047087 6 55 824808 234 871641 189 953167 423 046833 6 56 824949 234 871528 189 953421 423 046679 4 57 825090 234 871414 189 953675 423 046325 3 58 825230 234 871801 189 953929 423 046071 2 59 826371 234 871187 189 954183 423 04.5817 1 60 825511 234 871073 190 954437 423 045563 1 Cosine 1 SSine 1 Colanc i Tang. 1 M. 43 Degrees. 60 (42 Degrees.) a table of logaeithmic M. Sine D. r,... 1 n 1 Ta.:. 1 ^'• c... i 1 ~o" 9.8255111 234 j 9.871073! 190, 9.954437, 423 10.045563; 60 1 825651 233 1 870960 i90: 954691 423 0453091 59 2 825791 233 ! 8708461 ]90i 9.549451 423 04.50551 58 3 825931 2.33 1 870732! ]90i 955200 423 0448001 57 4 826071 233 ! 870618 190 9554.54 423 044546: 56 5 826211 233 1 870504 190 955707 423 044293! 55 6 826351 233 870390 190 955961 423 044039: 54 7 826491 2.33 870276 190 956215 423 043785! 53 8 826631 233 870161 190 956469 423 043531! 52 9 826770 232 870047 191 956723 423 0432771 51 10 11 826910 232 i 8699.33 9.869818 191 191 956977 423 0430231 10.042769' 50 49 9.827049 232 i 9.957231 423 12 827189 232 869704 191 957485 423 042515 48 13 827328 232 869589 191 957739 423 0422611 47 14 827467 232 869474 191 957993 423 0420071 46 15 827606 232 869360 191 958246 423 041754^ 45 16 827745 232 1 869245 191 958500 423 041. 500 i 44 17 827884 231 1 8691.30 191 95S754 423 0412461 43 18 828023 231 869015 192 959008 423 040992! 42 19 828162 231 86P900 192 959262 423 040738 ! 41 20 21 828301 231 666785 9.866670 192 192 959516 423 040484 40 39 9.828439 231 9.959769 423 10.040231 22 828578 231 868555 192 960023 423 039977: 38 23 828716 231 868440 192 960277 423 039723: 37 24 828855 230 868324 192 960531 423 039469; 36 25 828993 230 868209 192 960784 423 0392161 35 26 829131 230 868093 192 961038 423 038962! 34 27 829269 230 867978 193 961291 423 0387091 33 28 829407 230 867862 193 961.545 423 038455' 32 29 • 829545 230 867747 193 961799 423 0.38201; 31 30 31 829683 230 867631 9.867515 193 193 962052 423 037948; 10.037694^ 30 29 9.829S21 229 9.962306 423 32 829959 229 867399 193 962560 423 037440' 28 33 830097 229 867283 193 962813 423 037187 27 34 830234 229 867167 193 96.3067 423 036933 26 35 830372 229 867051 193 963320 423 036680 25 36 830509 229 866935 194 963574 423 036426 24 37 830546 229 866819 194 963827 423 036173 23 38 830784 229 866703 194 964081 423 035919 22 39 830921 228 866586 194 964335 423 035665 21 40 41 831058 228 866470 194 194 964588 422 035412 10.035158 20 19 9.831195 228 9.866353 9.964842 422 42 831332 228 866237 194 965095 422 0.34905 18 43 831469 228 866120 194 965349 422" 0.34651 17 44 831606 228 •866004 195 965602 422 034398 16 45 831742 228 865887 195 965855 422 034145 15 46 831879 228 865770 195 966109 422 033891 14 47 832015 227 865653 195 966362 422 033638 13 48 832152 227 865536 195 966616 422 033384 12 49 832288 227 865419 195 966869 422 033131 11 50 51 832425 227 865302 9.865185 195 195 967123 422 032877 10 9 9.832561 227 9.967375 422 10.032624 52 832697 227 865068 195 967629 1 422 032371 8 53 832833 227 864950 195 967883 422 032117 7 54 832969 226 864833 196 968136 422 031864 6 55 833105 226 864716 196 968389 422 031611 5 56 833241 226 864598 1 196 968643 422 JD31357 4 57 833377 226 864481 1196 968896 422 031104 58 ^ 833512 226 864363 196 969149 422 030851 2 59 833648 226 864245 196 969403 422 030597 1 60 83378S 226 864127 196 969656 422 i 030344 j Conine 1 1 Sine 1 I Crtar.H. ! 1 T:.. ,■ 47 Degrees. SINES AND TANGENTS (43 Degrees.) 61 1 Si:... 1 ^. 1 •, oj^.;;, 1 D. 1 Taiij;. D. i Co-..,g. 1 9.833783 226 1 9.864127 196 9.969656 422 10.030344,60 1 833919 225 864010 196 969909 422 030091 59 2 834054 225 863892 197 970162 422 029838 58 3 834189 225 863774 197 970416 422 029584 57 4 834325 225 863656 197 970669 422 029331 56 5 834460 225 863538 197 970922 422 0290781 55 6 834595 225 863419 197 971175 422 0288251 54 7 834730 225 863301 197 971429 422 028571 53 8 834865 225 863183 197 971682 422 028318 52 9 834999 224 863064 197 971935 422 028065 51 10 11 835134 224 862946 198 198 972188 422 027812 50 49 9.835269 224 9.862827 9.972441 422 10.027559 12 835403 224 862709 198 972694 422 027306 48 13 835538 224 862590 198 972948 422 027052 47 14 835672 224 862471 198 973201 422 026799 46 15 835807 224 862353 198 973454 422 026.546 45 16 835941 224 862234 198 973707 422 026293 44. 17 836075 223 862115 198 973960 422 026040 43 18 836209 223 861996 198 974213 422 025787 42 19 836343 223 861877 198 974466 422 025534 41 20 21 836477 223 861758 199 199 974719 9.974973 422 025281 10.025027 40 39 9.836611 223 9.861638 422 22 836745 223 861519 199 975226 422 024774 38 23 836878 223 861400 199 975479 422 024521 37 24 837012 222 861280 199 975732 422 024268 36 25 837146 222 861161 199 975985 422 024015 35 26 837279 222 861041 199 976238 422 023762 34 27 837412 222 860922 199 976491 422 023509 33 28 837546 222^ 860802 199 976744 422 023256 32 29 837679 222^ * 860682 200 976997 422 023003 31 30 31 837812 9.837945 222 860562 200 200 977250 422 022750 30 29 222 9.860442 9.977503 422 10.022497 32 838078 221 860322 200 977756 422 022244 28 33 838211 221 860202 200 978009 422 021991 27 34 838344 221 860082 200 978262 422 021738 26 35 838477 221 859962 200 978515 422 021485 25 36 838610 221 859842 200 978768 422 021232 24 37 838742 221 859721 201 979021 422 020979 23 38 838875 221 859601 201 979274 422 020726 22 39 839007 221 859480 2^' I 979527 422 020473 21 40 4i 839140 9.839272 220 859360 9.859239 201 201 979780 422 020220 10.019967 20 19 220 9.980033 422 42 839404 220 859119 201 980286 422 019714 18 43 839536 220 8.58998 201 9805.38 422 019462 17 44 839668 220 858877 201 980791 421 019209 10 45 839800 220 858756 202 981044 421 018956 15 46 839932 220 858635 202 981297 421 018703 14 47 840064 219 858514 202 981.550 421 018450 13 48 840196 219 858393 202 981803 421 018197 12 49 840328 840459 1 219 858272 202 982056 421 017944 11 50 51 ' 219 858151 9.858029 202 202 982309 421 017691 10 ! 9 9.840591 219 9.982.562 421 10.017438 52 840722 219 857908 202 982814 421 017186 8 53 840854 t 219 857786 202 98.3067 421 016933 7 54 84098? » 219 857665 20.3 98332C 421 016680 6 55 841116 ) 218 857543 203 983572 421 016427 5 56 84124^ r 218 857422 203 983826 421 016174 L 4 57 84137e i 218 85730C 202 98407£ ) 421 01.5921 3 58 841.50C ) 218 857178 20S 984331 421 015669 2 59 84164( ) 218 857056 202 98458^ t 421 01.5416 1 60 84177 L 218 8569341 202 98483' ' 421 015163 1 Cosine 1 j Sine 1 1 Cotanc 1 1 ""ang. 1 M. Degrees. 62 (44 Degrees.) a TABLE OF LOGARITHMIC s... .00 . '-■P 66.00 0.58 65.99 0.86 66 67 67.00 0.29 67.00 0.58 66.99 0.88 67 68 68.00 0.30 68.00 0.59 67.99 0.89 68 69 69 . 00 0.30 69.00 0.60 1 68.99 0.90 69 70 71 70.00 0.31 0.31 70.00 71.00 0.61 0.62 69.99 70.99 0.92 0.93 _70 71 71.00 72 72.00 0.31 72.00 0.63 71.99 0.94 72 73 73.00 0.32 73.00 0.64 72.99 0.96 73 74 74.00 0.32 74.00 0.65 73.99 0.97 74 75 75.00 0.33 75.00 0.65 74.99 0.98 75 76 76.00 0.33 76.00 0.66 75.99 0.99 76 77 77.00 0.34 77.00 0.67 1 76.99 . 1.01 77 78 78.00 0.34 78.00 0.68 77.99 1.02 78 79 79.00 0.34 79.00 0.69 78.99 1.03 79 80 80.00 0.35 80.00 0.70 79.99 1.05 80 81 81.00 0.35 81.00 0.71 80.99 1.06 81 82 82.00 0.36 82,00 0.72 81.99 1.07 82 83 83.00 0.36 83.00 0.72 82.99 1.09 83 64 84.00 0.37 84.00 0.73 83.99 I.IO 84 85 '^S.OO * 0.37 85.00 0.74 84.99 1.11 85 86 86.00 0.38 86.00 0.75 85.99 1.13 86 87 87.00 0.38 87.00 0.76 86.99 1.14 87 88 88.00 0.38 88.00 0.77 87.99 1.15 88 89 8G.00 0.39 89.00 0.78 88.99 1.16 89 90 90.00 0.39 SO. 00 0.79 89.99 1.18 90 91 91.00 0.40 91.00 0.79 90.99 1.19 9i 92 92.00 0.40 92.00 0.80 5]. 99 1.20 S2 93 93.00 0.41 93.00 C.81 ?2.99 ■ 1.22 93 94 94.00 0.41 94.00 0.82 93.99 1.23 94 95 95.00 0.41 95.00 0.83 94.99 1.24 95 96 G^ . 00 0.42 96.00 0.84 95.99 1.26 96 97 97.00 0.42 97.00 0.85 96.99 1.27 97 98 98.00 0.43 98.00 0.86 97.99 1.28« 98 99 99.00 0.43 99.00 0.86 98.99 1.30 99 100 100.00 0.44 100.00 0.87 99.99 1.31 100 1 Dep. Lat. Dep. 89^1 Lat. Deg. Dep. Lat. J 89 Deg. 89' I )eg. TRAVERSE I'ABLE. % 3 ? 1 1 Deg. H Deg. If Oeg, 1| Dtig, C Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1.00 0.O2 1.00 0.02 1.00 0.03 1.00 0.03 1 2 2.00 0.03 2.00 0.04 2.00 0,05 2.00 0.06 2 3 3.00 0.05 3.00 0.07 3.00 0.08 3.00 0.09 3 4 4.00 0.07 4.00 0.09 4.00 0.10 4.00 0.12 4 6 5.00 0.09 5.00 0.11 5.00 0.13 5.00 0.15 5 6 6.00 0.10 G.OO 0.13 6.00 0.16 6.00 0.18 6 7 7.00 0.12 7.00 0.15 7.00 0.18 7.00 0.21 7 8 8.00 0.14 8.00 0.17 8.00 0.21 8.00 0.25 8 9 9.00 0.16 9.00 0.20 9.00 0.24 9.00 0.28 9 10 11 10.00 11.00 0.17 07l9 10.00 0.22 10.00 0.26 10.00 0.31 10 11 11.00 0.24 11.00 0.28 10.99 0.34 12 12.00 0.21 12.00 0.26 12.00 0.31 11.99 0.37 12 13 13.00 0.23 13.00 0.28 13.00 0.34 12.99 0.40 13 14 14.00 0.24 14.00 0.31 14.00 0.37 13.99 0.43 14 15 15.00 0.26 15.00 0.33 14.99 0.39 14.99 0.46 15 16 16.00 0.28 16.00 0.,35 15.99 0.42 15.99 0.49 16 17 17.00 0.30 17.00 0.37 16.99 0.45 16.99 0.52 17 18 18.00 0.31 18.00 0.39 17.99 0.47 17.99 0.55 18 19 19.00 0.33 19.00 0.41 18.99 0.50 18.99 0.58 19 20 21 20.00 0.35 20.00 0.44 19.99 0.52 19.99 0.61 20 21 21.00 0.37 21.00 0.46 20.99 0.55 20.99 0.64 22 22.00 0.38 21.99 0.48 21.99 0.58 21.99 0.67 22 23 23.00 0.40 22.99 0.,50 22.99 0.60 22.99 0.70 23 24 24.00 0.42 23.99 0.52 23.99 0.63 23.99 0.73 24 25 25.00 0.44 24.99 0.55 24.99 0.65 24.99 0.76 25 26 26.00 0.45 25.99 0.57 25.99 0.68 25.99 0.79 26 27 27.00 0.47 26.99 0.59 26.99 0.71 26.99 0.83 27 2^ 28.00 0.49 27.99 0.61 27.99 0.73 27.99 0.86 28 29.00 0.51 28.99 0.63 28.99 0.76 28.99 0.89 29 30 "3] 30.00 0.52 0.54 29.99 0.65 29.99 0.79 29.99 0.92 30 31.00 30.99 0.68 30.99 0.81 30.99 0.95 31 32 32.00 0.56 31.99 0.70 31.99 0.84 31.99 0.98 32 33 32.99 0.58 32.99 0.72 32.99 0.86 32.98 1.01 33 34 33.99 0.59 33.99 0.74 33.99 0.89 33.98 1.04 34 35 34.99 0.61 34.99 0.76 34.99 0.92 34.98 1.07 35 36 35.99 0.63 35.99 0.79 35.99 0.94 35.98 l.iO 36 37 36.99 0.65 36.99 0.81 36.99 0.97 36.98 1.13 37 38 37.99 0.66 37.99 0.83 37.99 0.99 37.98 1.16 38 39 38.99 0.68 38.99 0.85 38.99 1.02 38.98 1.19 39 40 41 39.99 40.99 0.70 0.72 39.99 0.87 39.99 1.05 39.98 1.22 40 41 40.99 0.89 40.99 1.07 40.98 1.25 42 41.99 0.73 41.99 0.92 41.99 1.10 41.98 1.28 42 43 42.99 0.75 42.99 0.94 42.99 1.13 42.98 1.31 43 44 43.99 0.77 43.99 0.96 43.99 1.15 43.98 1.34 44 45 44.99 0.79 44.99 0.98 44.99 1.18 44.98 1.37 45 46 45.99 0.80 45.99 1.00 45.99 1.20 45.98 1.40 46 47 46^9 47^99 0.82 46.99 1.03 46.99 1.23 '46.98 1.44 47 48 0.84 47.99 1.05 47.98 1.26 147.98 1.47 48 49 48.99 0.86 48.99 1.07 48.98 1.28 148.98 1.50 49 50 0)* u C 5 49.99 Dep 0.87 49.99 1.09 49.98 1.31 149.98 1.53 60 .1 Lat. i>ep Lat. Dep. Lat. Dep. Lat. 89 J e.g. 88J Deg. ^^ Deg m Deg. TRAVERSE TABLE. i" "51 iii eg. li Deg. H Deg. 11 Deg. 5 Lat, Dep. Lat. Dep. Lat. 50.98 Dep. Lat. Dep. 50.99 0.89 50.99 1.11 1.34 50.98 1.56 "51 52 51.99 0.91 51.99 1.13 51.98 1.36 51.98 1.59 52 53 52.99 0.92 52.99 1.16 52.98 1.39 52.98 1.62 63 54 53.99 0.94 53.99 1.18 53.98 1.41 53.97 1.65 54 55 54.99 0.96 54.99 1.20 54.98 1.44 54.97 1.68 55 56 55.99 0.98 ,55.99 1.22 55.98 1.47 55.97 1.71 56 57 56.99 0.99 56.99 1.24 56.98 1.49 56.97 1.74 57 58 57.99 1.01 57.99 1.27 57.98 1.52 57.97 1.77 58 59 58.99 1.03 .58.99 1.29 58.98 1.54 .58.97 1.80 59 60 59.99 1.05 59.99 1.31 59.98 1.57 59.97 1.83 60 61 60.99 1.06 60.99 1.33 60.98 1.60 60.97 1.86 61 62 61.99 1.08 61.99 1.35 61.98 1.62 61.97 1.89 62 63 62.99 1 . 10 62.99 1.37 62.98 1.65 62.97 1.92 63 64 63.99 1.12 63.98 1.4C 63.98 1.68 63.97 1.95 64 65 64.99 1.13 64.98 1.42 64.98 1.70 64.97 1.99 65 66 65.99 1.15 65.98 1.44 65.98 1.73 65.97 2.02 66 67 66.99 1.17 66.98 1.46 66.98 1.75 66.97 2.05 67 68 67.99 1.19 67.98 1.48 67.98 1.78 67.97 2.08 68 69 68.99 1.20 68.98 1.51 68.98 1.81 66.97 2.11 69 70 71 69.99 70.99 1.22 69.98 1.53 69.98 1.83 69.97 70.97 2.14 2.17 70 71 1.24 70.98 1.55 70.98 1.86 72 71.99 1.26 71.98 1.57| 71.98 1.88 71.97 2.20 72 73 72.99 1.27 72.98 1.59 1 72.97 1.91 72.97 2.23 73 74 73.99 1.29 73.98 1.61 73.97 1.94 73.97 2.26 74 75 74.99 1.31 74.98 1.64 74.9.7 1.96 74.97 2.29 75 76 75.99 1.33 75.98 1.66 75.97 1.99 75.96 2.32 76 77 76.99 1.34 76.98 1.68 76.97 2.02 76.96 2.35 77 78 77.99 1.36 77.98 1.70 77.97 2.04 77.96 2.38 78 79 78.99 1.38 78.98 1.72 78.97 ti.07 78.96 2.41 79 80 81 79.99 80.99 1.40 1.41 7a. 98 80.98 1.75 79.97 80.97 2.09 2.12 79.96 2.44 80 81 1.77 80.96 2.47 82 81.99 1.43 81.98 1.79 81.97 2.15 81.96 2.50 82 83 82.99 1.45 82.98 1.81 82.97 2.17 82.96 2.53 83 84 83.99 1.47 83.98 1.83 83.97 2.20 83.96 2.57 84 85 84.99 1.48' 84.98 1.85 84.97 2.23 84.96 2.60 85 86 85.99 1..50 85.98 1.88 85.97 2.25 85.96 2.63 86 87 86.99 1.52 86.98 1.90 86.97 2.28 86.96 2.66 87 88 87.99 1.54 87.98 1.92 87.97 2.30 87.96 2.69 88 89 88.99 1.55 88.98 1.94 88.97 2.33 88.96 2.72 89 90 91 89.99 90.99 1.57 1.59 89.98 1.96 89.97 2.36 89.96 2.75 90 91 90.98 1.99 90.97 2.38 90.96 2.78 92 91.99 1.61 91.98 2.01 91.97 2.41 91.96 2.81 92 93 92.99 .1.62 92.98 2.03 92.97 2.43 92.96 2.84 93 94 93.99 1.64 93.98 2.05 93.97 2.46 93.96 2.87 94 95 94.99 .1.66 94.98 2.07 94.97 2.49 94.96 2.90 95l 96 95.99 1.68 95.98 2.09 95.97 2.51 95.96 2.94 96f 97 96.99 1.69 96.98 2.12 96.97 2.54 96.95 2.96. 971 98 97.99 1.71 97.98 2.14 97.97 2.57 97.95 2.99 98 99 98.98 1.73 98.98 2.16 98.97 2.59 98.95 3.02 99 100 .2 5 99.98 1.75 99.98 Hep 2.18 99.97 2.62 99.95 3.05 100 t? Q 1 : Dep. 1 Lat. Lat. Dep. Lat. Dep. Lat. 89 Deg. 1 88f Deff. 881 De^. 88i Deg. TRAVERSE TABLE. i - Oeg. 24 Deg. j 2} Beg. 21 ©eg. Lar Dep. Lat. Dep. Lat. Dep. Lat. Dep. 3 P 1 1.00 0.03 1.00 0.041 1.00 0.04 1 1.00 0.05 i 1 1 2 2.00 0.07 2.00 0.08 1 2,00 0.09 2.00 0.10 2 1 3 3.00 0.10 3.00 0.12i 3.00 0.13 3.00 0.14 3 4 4.00 0.14 4.00 0.16! 4.00 0.17, 4.00 0.19 4 5 5.00 0.17 5.00 0.20: 5.00 0.22 4.99 0.24 5 6 6.00 0.21 6.00 0.24, 5.99 0.26 5.99 0.29 i 6 7 7.00 0.24 6.99 0.27i! 6.99 0.31 6.99 0.34 7 8 7.99 0.28 7.99 0.31 1 7.99 0.351 7.99 0.38 j 8 9 8.99 0.31 8.99 0.35 1 8.99 0.39' 8.99 0.43! 9 10 t 9.99 11 i 10.99 0.35 9.99 0.39 1 9.99 10.99 0.44; 9.99 0.48! 10 0.38 j 10.99 0.43 1 0.48! 10.99 0.53 11 12 1 11.99 0.42 1 11.99 0.47 1 11.99 0.52' 11.99 0.58 12 13 ! 12.99 0.45 12.99 0.51 ! 12.99 0.57 12.99 0.62 13 14! 13.99 0.49 ;. 13.99 0.55 1 13.99 0.61 ! 13.98 0.67 14 15 i 14.99 0..52 |l 14.99 0..59 I 14 = 99 0.65'! 14.98 0.72 15 16 15.99 0.56 |! 15.99 0.63 15.99 0.70 I 15.98 0.77 16 17U6.99 0.59 J! 16.99 0.67 11 16.98 0.74 ;i 16.98 0.82 17 IS i 17.99 0.63 - 17.99 0.71 ; 17.98 0.79;' 17.98 0.86 i 18 19 t 18.99 0.66 • 18.99 0.75 i 18.98 0.83 i 18.98 0.91 ; 19 20 ! 19.99 21 20.99 0.70 1 19.98 0.79! 19.98 20.98 0.87 0.92 ! 19.98 0.96 20 0.73 '20.98 0.82 1 20.98 1.01 21 22:21.99 0.77 21.98 0.86! 21.98 0.96 21.97 1.06 23 i 22.99 0.80 122.98 0.90 22.98 1.00 22.97 1.10 23 24 23.99 0.84;; 23.98 0.94 ; 23.98 1.05 23.97 1.15 24 25 124.98 O.S7| 24.98 0.98 i 24.98 1.09 124.97 1.20 25 26 i 25.98 0.91 i 25.98 1.02;! 25.98 1.13 25.97 1.25 26 27 126.98 0.941 26.98 1.06 !, 26.97 1.18 ; 26.97 1.30 27 28 127.98 0.98 27.98 1.10 ;! 27.97 1.22 : 27.97 1.34 28 29 128.93 1.01 28.98 1. 14 1! 28.97 1.26 1128.97 1.39 29 30 129.98 1.05 29.98 1.181 1.22 29.97 l.«l i.i 29.97 1.44 30 31 ! 30.98- 1.08 30.98 30.97 1.35 j! .30.96 1.49 31 32 131.98 1.12: 31.98 1.26 ■ 31.97 1.40 1,: 31.96 1.54 32 33 132.98 1.15 1 32.97 1.30 ! 32.97 1.441 32.96 1..58 33 34 133.98 1.19 |! 33.97 1.33 li 33.97 1.43 1.33.96 1 .63 j 34 35 34.98 1.22 34.97 1.37 34.97 1..53 134.96 1.68 ! 35 36 35.98 1.26! 35.97 1.41 35.97 1.57 135.96 1.73 1 36 37 36.98 1.29! 36.97 1.45 36.96 1,61 1-36.96 1.78 37 38 137.98 1.33 37.97 1.49 37.96 1.66 ;37.96 1.82 38 39 38.98 1.36 .38.97 1 . .=i3 1' .38 . 96 1.70 [38.96 1.87 39 40 41 39.98 40.98 1.40 1 1.43 j 39.97 1.57 .39.96 40.96 1.75 1.77 39.95 1.92 i 40 1 40.97 1.61 140.95 1.97 j 41 1 42 41.97 1.47 1141.97 1.65 1141.96 1.83 141.95 2.02 42 43 42.97 1.50, 42.97 1.69 ii 42.96 1.73 43.96 1.88 142.9^ 2.06 43 44 43.97 1..54 43.97 1.92 143.95 2.11 44 45 144.97 1.57 44.97 1.77 : 44.96 1.81 145.96 1.96 ! 44.95 2.16 4?) 46 i 45.97 1.61 45.96 2.01 !l 45.95 2.21 46 47 46.97 1.64 46,96 1.85 ! 46.96 2.05 il 46.95 2.25 47 48 147.97 1.68 47.96 1.88 147.95 2.09! 47.95 2.30 48 49 ! 48.97 1.71 48.96 1.92 '48.95 2. 14 11 4«. 94 2.35 49 50 49.97 1.74 149.96 1.96 !| 49.95 2.18 11 49. 94 2.40 50 § Dep. Lat. Dep. 875 Lat. De£r. Dep Lat. Dep • at. 1 en Deg 87i Deg. ! H7^ Desr. TRAVERSE TABLE. 2 2 Deg. 2i Deg. n Deg. 21 Deg. 3 ? 51 Lat. Dep. Lat. Dep. 1 Lat L>ep. Lat. Dep. 50.97 1.78 50.96 2.00 50.95 2.22 50.94 2.45 52 51.97 1.81 51.96 2.04 51.95 2.27 51.94 2.50 52 53 52.97 1.85 52.96 2.08 52.95 2.31 52.94 2.54 53 54 53.97 1.88 53.96 2.12 53.95 2.36 53.94 2.59 54 55 54.97 1.92 54.96 2.16 54.95 2.40 54.94 2.64 55 56 55.97 1.95 55.96 2.20 55.95 2.44 55.94 2.69 56 57 56.97 1.99 56.96 2.24 56.95 2.49 56.93 2.73 57 58 57.96 2.02 57.96 2.28 57.94 2.53 57.93 2.78 58 59 58.96 2.06 58.95 2.32 58.94 2.57 58.93 2.83 69 60 61 59.98 2.09 59.95 2.36 59.94 2.62 59.93 2.88 60 61 60.96 2.13 60.95 2.39 60.94 2.66 60.93 2.93 62 61.96 2.16 61.95 2.43 61.94 2.70 61.93 2.97 62 , 63 62.96 2.20 62.95 2.47 62.94 2.75 62.93 3.02 63 64 63.96 2.23 63.95 2.51 63.94 2.79 63.93 3.07 64 65 64.96 2.27 64.95 2.55 64.94 2.84 64.93 3.12 65 66 65.96 2.30 65.95 2.59 65.94 2.88 65.92 3.17 66 67 66.96 2.34 66.95 2.63 66.94 2.92 66.92 3.21 67 68 67.96 2.37 67.95 2.67 67.94 2.97 67.92 3.26 68 69 68.96 2.41 68.95 2.71 68.93 3.01 68.92 3.31 69 70 71 69.96 2.44 69.95 2.75 69.93 3.05 69.92 3.36 70 71 70.96 2.48 70.95 2.79 70.93 3.10 70.92 3.41 72 71.96 2.51 71.94 2.83 71.93 3.14 71.92 3.45 72 73 72.96 2.55 72.94 2.87 72.93 3.18 72.92 3.50 73 74 73.95 2.58 73.94 2.91 73.93 3.23 73.91 3.55 74 75 74.95 2.62 74.94 2.94 74.93 3.27 74.91 3.60 75 76 75.95 2.65 75.94 2.98 75.93 3.31 75.91 3.65 76 77 76.95 2.69 76.94 3.02 76.93 3.36 76.91 3.70 77 78 77.95 2.72 77.94 3.06 77.93 3.40 77.91 3.74 78 79 78.95 2.76 78.94 3.10 78.92 3.45 78.91 3.79 79 80 81 79.95 2.79 ' 79.94 3.14 79.92 3.49 79.91 3.84 80 81 80.95 2.83' 80.94 3.18 80.92 3.53 80.91 3.89 83 81.95 2.86 81.94 3.22 81.92 3.58 81.91 3.93 82 83 82.95 2.90 82.94 3.26 82.92 3.62 82.90 3.98 83 84 83.95 2.93 83.94 3.30 83.92 3.66 83.90 4.03 84 85 84.95 2.97 §4.93 3.34 84.92 3.71 84.90 4.08 85 86 85.95 3.00 85.93 3.. 38 85.92 3.75 85.90 4.13 86 87 86.95 3.04 86.93 3.42 86.92 3.79 86.90 4.17 87 88 87.95 3.07 87.93 3.45 87.92 3.84 87.90 4.22 88 89 88.95 3.11 88.93 3.49 88.92 3.88 88.90 4.27 89 90 91 89.95 3.14 89.93 3.. 53 89.91 3.93 89.90 4.32 90 91 90.95 3.18 90.93 3.57 90.91 3.97 90.90 4.37 92 91.94 3.21 91.93 3.61 91.91 4.01 91.89 4.41 92 93 92.94 3.25 92.93 3.65 92.91 4.06 92.89 4.46 93 94 93.94 3.28 93.93 3.69 93.91 4.10 93.89 4.51 94 95 94.94 3.32 94.93 3.73 94.91 4.14 94.89 4.56 95 96 95.94 3.35 95.93 3.77 95.91 4.19 95.89 4.61 96 97 96.94 3.39 96.93 3.81 96.91 4.23 96.89 4.65 97 98 97.94 3.42 97.92 3.85 97.91 4.27 97.89 4.70 98 99 98.94 3.46 98.92 3.89 98.91 4.32 98.89 4.75 99 100 c 5 99.94 3.49 99.92 3.93 99.91 4.36 99.88 4.80 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 88 Deg. 87| Deg. 871 Deg. 874 Deg. TRAVERSE TAELE. i 1 3Deg. 3iJ Deg. , 3|De,. 31 Deg. i 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1.00 0.05 1.00 0.06 1.00 0.06 1.00 0.06 2 2.00 0.10 2.00 0.11 3.00 0.12 2.00 0.13 2 3 3.00 0.16 3.00 0.17 2.99 0.18 2.99 0.20 3 4 3.99 0.21 3.99 0.23 3.99 0.24 3.99 0.26 4 5 4.99 0.26 4.99 0.38 4.99 0.31 4.99 0.33 5 6 5.99 0.31 5.99 0.34 5.99 0.37 5.99 0.39 6 7 6.99 0.37 6.99 0.40 6.99 0.43 6.99 0.46 7 8 7.99 0.42 7.99 0.45 7.99 0.49 7.98 0.52 8 9 8.99 0.47 8.99 0.51 8.98 0.55 8.98 0..59 9 10 9.99 0.52 9.98 0.57 9.98 0.61 9.98 0.65 10 11 11 10.98 0..58 j 10.98 0.63 10.98 0.67 10.98 0.72 13 11.98 0.63! 11.98 0.68 11.98 0.73! 11.97 0.78 12 13 12.98 0.68 j 12.98 0.73 12.98 0.79 12.97 0.85 P 14 14 13.98 0.73 13.98 0.79 13.97 0.85) 13.97 0.92 15 14.98 0.79' 14.93 0.85 14.97 0.92, 14.97 0.98 15 16 i 15.98 0.841 15.97 0.91 15.97 0.98 15.97 1.05 16 17 i 16. 9S 0.89 1 16.97 0.96 16.97 1.04 16.96 1.11 17 is! 17.98 0.94! 17.97 1.02 17.97 1.10 17.96 1.18 18 19 i 18.98 0.99! 18.97 1.08 18.96 1.16 18.96 1.24 19 20 19.97 1.05 19.97 1.13_ 19.96 1.22 19.96 1.31 20 21 21 20.97 1.10 20.97 1.19 20.96 1.28 1 20.96 1.37 22 1 21.97 1.15 : 21.96 1.35 21.96 1.34 21.95 1.44 22 28 1 22.97 1.20, 23.96 1.30 22.96 1.40 22.95 1.50 23 24 1 23.97 1.23 33.98 1.38 23.96 1.47 23.95 1.57 24 25 1 24.97 1.31 34.96 1.43 24.95 1.53 24.95 1.64 25 26! 25.96 1.36 25.96 1.47 25.95 1.59 25.94 1.70 26 27 26.96 1.41 26.96 1.53 26.95 1.65 26.94 1.77 27 28) 27.96 1.47 27.95 1.59 137.95 1.71 ! 27.94 1.83 28 29 ; 28.93 1.52 28.95 1.64 ,38.95 1.77: 28.94 1.90 29 30 29.96 1..57 29.95 1.70 39.94 1.83 29.94 1.96 30 31 31 30.96 1.62! 30.95 1.76 30.94 1.89 30.93 2.03 32 31.98 1.67; 31.95 1.81 31.94 1.95 31.93 2.09 32 33 33.95 1.73; 32.95 1.87 133.94 2.01 32.93 2.16 33 34 33.95 1.78: 33.95 1.93 33.94 2.08! 33.93 2.22 34 35 34.95 1.83: 34.94 1.98 134.93 2.14; 34.93 2.29 35 36 35.95 1.8S 35.94 3.04 135.93 2.20: 35.92 2.35 36 37 36.95 1.9i 36.94 2.10 136.93 2.26 ! 36.92 2.42 37 33 37.95 1.99 37.94 2.15 137.93 3.33 37.92 2.49 38 39 38.95 2.04 33.94 2.21 138.93 2.38 38.92 2.55 39 40 39.95 2.09 39 . 94 2.27 2.32 39.93 2.44 39.91 2.62 40 41 41 40.94 2.15.1 40.93 40.92 2.50 40.91 2.68 42 i 41 . 94 2.20 41.93 2.38 141.92 2.56 41.91 2.75 42 43 42.94 2.25 42.93 2.44:142.92 2.63 42.91 2.81 43 44 i 43.94 2.30 43.93 2.49 143.92 2.69 43.91 2.88 44 45! 44.94 2.36 44.93 2.55 144.92 2.75 44.90 2.94 45 46 1 45 . 94 2.41 45.93 2.61 145.91 2.81 45.90 3.01 46 47:46.94 2.46 46.92 2.68,146.91 2.87, 46.90 3.07 47 43 i 47.93 2.51 47.92 2.73 147.91 2.93 47.90 3.14 48 49 148.93 3.. 56 48.92 3. 78 ii 48.91 2.99 48.90 3.20 49 _50 49.93 2.63 Lat. 49.92 3.83 49.91 3.05 49.89 3.27 50 1 .5 d o Dep. Dep. Lat. I Dep. Lat. Dep. Lat. 87 1 )eg. 861 Deg. 86^ Deg. 86^ Deg. :<.^^m^mm^ TRAVERSE TABLE. OS i 51 3Deg. 3i Deg. ^ Deg. 3| Deg. 3 ? 51 Lat. Dep. Lat. 50.92 Dep. Lat Dep. Lat. Dep. 50.93 2.67 2.89 50.90 3.11 50.89 3.34 52 51.93 3.72 ! 51.92 2.95 51.90 3.17 51.89 3.40 52 53 52.93 2.77 52.91 3.00 52.90 3.24 52.89 3.47 53 54 53.93 2.83 ; 53.91 3.06 53.90 3.30 53.88 3.53 54 65 54.92 2.88 i 54.91 2.93 ,55.9 3.12 54.90 3.36 54.88 3.60 55 56 55.92 3.17 55.90 3.42 55.88 3.66 56 57 56.92 2.98 ,56.91 3.23 156.89 3.48 56.88 3 73 57 58 57.92 3.04 157.91 3.29 157.89 3.54 57.88 3.79 68 59 58.92 3.09 i 58.91 3.34 58.89 3.60 58.87 3.86 59 60 59.92 3.14 ii 59.90 3.40 59.89 3.66 59.87 3,92 60 61 60.92 3.19 ;! 60.90 3.46 60.89 3.72 60.87 3.99 6] 62 61.92 3.24 1161.90 3.51 61.88 3.79 61.87 4.05 62 63 62.91 3.30 62.90 3.57 62.88 3.85 62.87 4.12 63 64 63.91 3.35 63.90 3.63 63.88 3.91 63.86 4.19 64 65 64.91 3.40 164.90 3.69 64.88 3.97 64.86 4.25 65 66 65.91 3.45 165.89 3.74 65.88 4.03 65.86 4.32 66 67 66.91 3.51 66.89 3.80 66.88 4 09 66.86 4.38 67 68 67.91 3.56 67.89 3.86 ,67.87 4.15 67.85 4.45 68 69 68.91 3.61 68.89 3.91 68.87 4.21 68.85 4.51 69 70 71 69.90 3.66 69.89 3.97 69.87 4 27 4.33 69.85 4.58 70 Tl 70.90 3.72 70.89 4.03 70.87 70.85 4.64 72 71.90 3.77 '71.88 4.08 171.8? 4.40 71.85 4.71 72 73 72.90 3.82 72.88 4.14 72.86 4.46 72.84 4.77 73 74 73.90 3.87,. 73.88 4.20 73.86 4.52 73.84 4.84 74 75 74.90 3.93 74.88 4.25 74.86 4.58 74.84 4.91 75 76 75.90 3.98 75.88 4.31 75 86 4.64 75.84 4-97 76 77 76.89 4.03 76.88 4.37 76.86 4.70 176.84 5.04 77 78 77.89 4.08 77.87 4.42 77.85 4.76 1 77.83 5.10 78 79 78.89 4.13 78.87 4.48 78.85 4.82 i 78.83 5.17 79 80 81 79.89 4.19 79.87 4.54 79.85 4.88 179.83 5.23 80 81 80.89 4.24 80.87 4.59 80.85 4.94 1 80.83 5.30 82 81.89 4.29 81.87 4.65 81.85 5.01 81.82 5.36 82 83 82.89 4.34 82.87 4.71 82.85 5.07 82.82 5.43 83 84 83.88 4.40 83.86 4 76 83.84 5.13 183.82 5.49 84 85 84.88 4.45 84.86 4.82 84.84 5.19 184.82 5.56 ■85 86 85.88 4.50 85.86 4 88 85.84 5.25 185.82 5.62 86 87 86.88 4.55 86.86 4.93 §£.84 ^.84 5.31 i 86.81 5.69 87 88 87.88 4.61 87.86 4.99 5.37 87.81 5.76 88 89 88.88 4.66 88.86, 5.05 88.83 5.43 188.81 5.82 89 90 91 89.88 4.71 89.86 5.10 5.16 89.83 5.49 189.81 5.89 90 91 90.88 4.76 90.85 90.83 5.56 90.81 5.95 92 91.87 4.81 91.85 5.22 91.83 5.62 91.80 6.02 92 93 92.87 4.87 92.85 5.27 92.83 5.68 92.80 6.08 93 94 93.87 4.92 93.85 5.33 93.82 5.74 93.80 6.15 94 95 94.87 4.97 94.85 5.39 94.82 5.80 94.80 6.21 95 96 95.87 5.02 95.85 5.44 95.82 5.86 95.79 6.28 96 97 96.87 5.08 96.84 5.50 96.82 5.92 96.79 6.34 97 98 97.87 5.13 97.84 5.56 97.82 5.98 97.79 6.41 98 99 98.86 5.18 98.84 5.61 98.82 6.04 98.79 6.47 99 100 99.86 5.23 99.84 5.67 99.81 6.10 99.79 6.54 100 .5' Q Dep. Lat. Dep. Lat. Dep. Lat, Dep. Lat. 87 r )eg. 861 ] Deg. 66^3 Deg". 86^ Deg. 10 TEAVEHSE TABLE. 1 ~1 4 Deg. 4iDeg. [ ! 4^ Deg. 1 li 4t Deg. Lat. Dep. C 1 Lat. Dep. Lat. Dep. 1 Lat. 1.00 Dep. 1 1.00 0.07 1.00 0.07 0.08 1.00 0.08 2 2.00 0.14 1.99 0.15 1.99 0.16 1.99 0.17 2 3 2.99 0.21 2.99 0.22 1 2.99 0.24 2.99 0.25 3 4 3.99 0.28 3.99 0.30 3.99 0.31 I 3. 98 0.33 4 5 4.99 0.35 4.99 0.37 4.98 0.39 1 4.98 0.41 5 6l 5.99 0.42 11 5.98 0.44 5.98 0.471 5 . 98 0.50 6 7 6.98 0.49 6.98 0.52 6.98 0.55 6.97 0.58 7 8 7,98 0.56 7.98 0.59 7.98 0.63 1 7.97 0.66 8 9 8.98 0;63 8.98 0.67 8.97 0.71 8.97 0.75 9 10 1 11 9.98 0.70 9.97 0.74 9.97 0.78 9.97 0.83 10 11 10.97 i 0.77 10.97 0.82 10.97 0.86 10.96 1 0.91 12 11.97 0.84 11.97 0.89 11.96 0.94 11.96 0.99 12 13 12.97 0.91 12.96 0.96 12.96 1.02 12.96 1 1.08 13 14 13.97 0.98 13.96 1.04 13.96 1.10 13.95 1 1.16 14 15 14.96 1.05 14.96 1.11 14.95 1.18 14.95 1.24 15 16 15.96 1.12 15.96 1.19 15.95 1.26 15.95 1.32 16 17 16.96 1.19 16.95 1.26 16.95 1.33 1 16.94 1.41 17 18 17.96 1.26 17.95 1.33 17.94 1.41 17.94 1.49 18 19 18.95 1.33 18.95 1.40 18.94 1.49 18.93 1.57 19 20 21 19.95 1.40 19.95 1.48! :.94 :. .94 1.57 19.93 1.66 20 21 20.95 1.46 20.94 1.56 1.65 20.93 1.74 22 21.95 1.53 21.94 1.63 21.93 1.73 21.92 1.82 22 23 22.94 1.60 22.94 1.70 22.93 1.80 22.92 1.90 23 24 23.94 1.67 23.93 1.78 23.93 1.88 23.92 1.99 24 25 24.94 1.74 24.93 1.85 24.92 1.96 24.91 2.07 25 26 25.94 1.81 25.93 1.93 25.92 2.04 25.91 2.15 26 27 26.93 1.88 26.93 2.00 26.92 2.12 26.91 2.24 27 28 27.93 1.95 27.92 2.08 27.91 2.20 1 27.90 2.32 28 29 28.93 2.02 28.92 2.15 28.91 2.28 28.90 2.40 29 30 31 29.93 1 2.09 29.92 2.22 29.91 2.35 29.90 2.48 30 31 30.92 2.16 30.91 2.30 30.90 2.43 ."0.89 2.57 32 31.92 2.23 31.91 2.37 31.90 2.51 31.89 2.65 32 33 32.92 2.30 32.91 2.45 32.90 2.59 32.89 2.73 33 34 133.92 2.37 33.91 2.52 33.90 2.67 33.88 2.82 34 35 134.91 2.44 34.90 2.59 34.89 2.75 34.88 2.90 •35 36 135.91 2.51 35.90 2.67 35.89 2.82 35.88 2.98 36 37 ,36.91 2.58 36.90 2.74 36.89 2.90 36.87 3.06 37 38 1 37.91! 2.65 37.90 %.82 37.88 2.98 37.87 3.15 38 39 138.90 I 2.72 38.89 2.89 38.88 3.06 38.87 3.23 39 40 139.90; 2.79 39.89 2.96 39.88 3.14 39.86 3.31 40 41 i 40.90 1 2.86 40.89 3.04 40.87 3.22 40.86 3.40 41 42 141.90 2.93 41.88 3.11 41.87 3.30 41.86 3.48 42 43 '42.901 3.00 42.88 3.19 42.87 3.37 42.85 3.56 43 44 143.89' 3.07 43.88 3.26 43.86 3.45 43.85 3.64 44 45 .44.89: 3.14 44.88 3.33 44.86 3.53 44.85 3.73 45 46 145.89' 3.21 45.87 3.41 45.86 3.61 45.84 3.81 46 47 146.89, 3.28 46.87 3.48 46.86 3.69 46.84 3.89 47 48 147.88 ! 3.35 47.87 3.56 47.85 3.77 47.84 3.97 48 49 148.88 8.42 48.87 3.63 48.85 3.84 48.83 4.06 49 _50 © 1 1 49.88 3.49 49.86 3.71 49.85 3.92 49.83 4.14 50 i 1 .2 Dep. Lat. Dep. Lat. Dep. , Lat. Dep. Lat. 86 Deg. 1 85J Deg. 11 851 Deg. 85i Deg. TKAVEKSE TABLE. 11 P 51 4 Deg. 4i Deg. 4i Deg. 4| Deg. "51 Lat. Dep. Lat. 50.86 Dep. ! Lat. Dep. Lat, Dep. 50.88 3.56 3,78 50.84 4.00 50.82 4.22 52 51.87 3.63 51.86 3,85 51,84 4.08 51,82 4.31 52 53 52.87 3.70 52.85 3,93 52,84 4.16 52.82 4.39 53 54 53.87 3.77 53.85 4.00 53,83 4.24 53.81 4.47 64 55 54.87 3.84 54.85 4.08 54,83 4.32 54.81 4.55 55 56 55.86 3,91 55.85 4.15 55,83 4.39 55.81 4.64 56: 57 56.86 3.98 56.84 4.22 56.82 4.47 56.80 4.72 67 58 57.86 4.05 57.84 4.30 57.82 4,55 57.80 4.80 58 59 '58.86 4.12 58.84 4.37 58.82 4.63 58.80 4.89 59 60 61 59.85 4.19 59.84 4.45 59.82 4,71 59.79 4.97 6o; 61 60.85 4.26 60.83 4.52 60.81 4,79 60,79 5.05 62 61.85 4.32 61.83 4.59 61.81 4,86 61.79 5.13 62; 63 62.85 4.39 62.83 4.67 62.81 4.94 62.78 5.22 63i 64 63.84 4.46 63.82 4.74 63.80 5.02 63.78 5.30 64j 65 64.84 4.53 64.82 4.82 64.80 5.10 64.78 5.38 65i 66 65.84 4.60 65.82 4.89 65.80 5.18 65.77 5.47 66: 67 66.84 4.67 66.82 4.97 66.79 5.26 66.77 5.55 67 68 67.83 4.74 67.81 5.04 67,79 5.34 67.77 5.63 68 69 68.83 4.81 68.81 5.11 68,79 5.41 68.76 5.71 69 70 71 69.83 4.88 69.81 5.19 69,78 5,49 69.76 5.80 70 7L 70.83 4.95 70.80 5.26 70.78 5.57 70.76 5.88 72 71.82 5.02 71.80 5.34 71,78 5.65 71.75 6.96 72 73 72.82 5.09 72.80 5.41 72.77 5.73 72.75 6.04 73 74 73.82 5.16 73.80 5.48 73,77 5,81 73.75 6.13 74i 75 74.82 5.23 74.79 5.56 74,77 5.88 74.74 6.21 76; 76 75.81 6.30 75.79 5.63 75,77 5.96 75.74 6.29 76; 77 76.81 5.37 76.79 5.71 76,76 6.04 76.74 6.38 77; 78 77.81 5.44 77.79 5.78 77.76 6.12 77.73 6.46 78 79 78.81 5.51 78.78 5.85 78.76 6.20 78.73 6.54 79 80 81 79.81 5.58 79.78 5.93 79.75 6.28 79.73 6.62 8OI 81^; 80.80 5.65 80.78 6.00 80.75 6.36 80.72 6.71 82 81.80 5,72 81.78 6.08 81.75 6,43 81.72 6.79 82 83 82.80 5,79 82.77 6.15 82.74 6.51 82.71 6.87 83' 84 83.80 5.86 83.77 6.23 83.74 6.59 83.71 6.96 84 85 84.79 5.93 84.77 6.30 84.74 6.67 84.71 7.04 85 86 85.79 6.00 85.76 6.37 85.73 6.75 85.70 7.12 86 87 86.79 6.07 86.76 6.45 86.73 6.83 80.70 7.20 87. 88 87.79 6.14 87.76 6.52 87.73 6.90 87.70 7.29 88 89 88.78 6.21 88.76 6.60 88,73 6.98 88.70 7.37 89 90 91 89.78 6.28 89.75 90.75 6.67 89,72 7.06 89.69 7.45 90 91 90.78 6.35 6.74 90.72 7.14 90.69 7.54 92 91.78 6.42 91.75 6.82 91.72 7.22 91.68 7.62 92 93 92.77 6,49 92.74 6.89 92.71 7.30 92.68 7.70 93: 94 93,77 6.56 93.74 6.97 93.71 7.38 93.68 7.78 94 95 94.77 6.63 94.74 7.04 94.71 7.45 94.67 7.87 95 96 95.77 6.70 95.74 7.11 95.70 7.53 95.67 7.96 96 97 96.76 6.77 96,73 7.19 96.70 7.61 96.67 8.03 97 98 97.76 6.84 97.73 7.26 97.70 7.69 97.66 8.12 98 99 98.76 6.91 98.73 7.34 98.69 7.77 98.66 8.20 99 100 i 1 99.76 6.98 99.73 7.41 99.69 7.85 99.66 8.28 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep, Lat. c ■ 861 )eg. 851 ] >eg. 85^ Deg. j - 85i Deg. .2 Q 12 TRAVERSE TABLE, u - s §, 1 5Deg. 5i D 1 eg. 5| Deg. 1 5J Deg. 5 3 o re Lat. 1 Dep. 0.09 Lat. Dep. Lat. Dep. Lat. Dep. 1.00 1.00 0.09 1.00 0.10 0.99 0.10 1 2 1.99 0.17 1.99 0.18 1.99 0.19 1.99 0.20 2 3 2.99 0.26 2.99 0.27 2.99 0.29 2.98 0.30 3 4 3.98 0.35 3.98 0.37 3.98 0.38 3.98 0.40 4 5 4.98 0.44 4.98 0.46 4.98 0.48 4.97 0.50 5 6 5.98 0.52 5.97 0.55 5.97 0.58 5.97 0.60 6 7 6.97 0.61 0.97 0.64 6.97 0.67 6.96 0.70 7 8 7.97 0.70 7.97 0.73 7.96 0.76 7.96 0.80 8 9 8.97 0.78 8.96 0.82 8 96 0.86 8.95 0.90 9 12_ 11 9.96 0.87 9.96 0.92 9.95 0.96 9.95 1.00 10 11 10.96 0.96 10.95 1.01 10.95 1.05 10.94 1.10 12 11.95 1.05 11.95 1.10 11.94 1.15 11.94 1.20 12 13 12.95 1.13 12.95 1.19 12.94 1.25 12.93 1.30 13 14 13.95 1.22 13.94 1.28 13.94 1.34 13.93 1.40 14 15 14.94 1.31 14.94 1.37 14.93 1.44 14.92 1.50 15 16 15.94 1.39 15.93 1.46 15.93 1.53 15.92 1.60 16 17 16.94 1.48 16.93 1.56 16.92 1.63 16.91 1.70 17 IS 17.93 1.57 17.92 1.65 17.92 1.73 17.91 1.80 18 19 18.93 1.66 18.92 1.74 18.91 1.82 1 18.90 1.90] 19 20 21 19.92 1.74 19.93 1.83 19.91 1.92 19.90 2.00 20 20.92 1.83 20.91 1.92 20.90 2.01 20.89 2.10 21 22 21.92 1.92i 21.91 2.01 21.90 2.11 21.89 2.20 22 23 22.91 2.00 22.90 2.10 22.89 2.20 22.88 2.30 23 24 23.91 2.09 23.90 2.20 23.89 2.30 23.88 2.40 24 25 24.90 2.18 24.90 2.29 24.88 2.40 24.87 2.50 25 26 25.90 2.27 25.89 2.38 25.88 2.49 25.87 2.60 26 27 26.90 2.35 26.89 2.47 26.88 2.59 26.86 2.71 27 28 27.89 2.44 27.88 2.56 27.87 2.68 27.86 2.81 28 29 28.89 2.53 28.88 2.65 28.87 2.78 28.85 2.91 29 30 31 29.89 2.61 29.87 2.75 2.84 29.86 2.88 29.85 3.01 30 30.88 2.70 30.87 30.86 2.97 30.84 3.11 31 32 31.88 2.79 31.87 2.93 31.85 3.07 31.84 3.21 32 33 32.87 2.88 32.86 3.02 32.85 3.16 32.83 3.31 33 ^ 34 33.87 2.96 33.86 3.11 33.84 3.26 33.83 3.41 34 35 34.87 3.05 34.85 3.20 34.84 3.35 34.82 3.51 35 '36 35.86 3.14 35.85 3.29 35.83 3.45 35.82 3.61 36 ■ 37 36.86 3.22 36.84 3.39 36.83 3.55 36.81 3.71 37 \ 38 37.86 3.31 37.84 3.48 37.83 3.64 37.81 3.81 38 39 38.85 3.40 38.84 3.57 38.82 3.74 38.80 3.91 39 ,40 41 39.85 3.49 39.83 3.66 39.82 3.83 39.80 4.01 40 41 40.84 3.57 40.83 3.75 40.81 3.93 40.79 4.11 : 42 41.84 3.66 41.82 3.84 41.81 4.03 41.79 4.21 42 43 42.84 3.75 42.82 3.93 42.80 4.12 42.78 4.31 43 44 43.83 3.83 43.82 4.03 43.80 4.22 43.78 4.41 44 45 44.83 3.92 44.81 4.12 44.79 4.31 44.77 4.51 45 46 45.82 4.01 45.81 4.21 45.79 4.41 45.77 4.61 46 47 46.82 4.10 146.80 4.30 46.78 4.50 46.76 4.71 47 48 47.82 4.18 47.80 4.39 47.78 4.60 47.76 4.81 48 49 48.81 4.27 48.79 4.48 48.77 4.70 48.75 4.91 49 50 49.81 4.36 49.79 4.58 49.77 4.79 49.75 5.01 50 Deli. \ Lat. Dep. Lat. Dep. Lat. Dep. Lat. i 85Deg. 841 Deg. 841 Deg. 844 Deg. .a TRAVERSE TABLE. IS a 51 5Deg. 5i Deg. . Deg. 51 Deg. O Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 50.81 4,44 50.79 4.67 50.77 4.89 60.74 6.11 "ti 52 51.80 4.53 51.78 4.76 61.76 4.98 61.74 5.21 52 53 52.80 4.62 52.78 4.85 52.76 5.08 52.73 6.31 53 54 53.79 4.71 53.77 4.94 53.75 5.18 63.73 6.41 54 55 54.79 4.79 54.77 5.03 64.76 5.27 54.72 5.51 55 56 55.79 4.88 55.77 5.12 55.74 6.37 55.72 6.61 66 57 56.78 4.97 56.76 5.22 66.74 6.46 56.71 5.71 57 58 57.78 5.06 57.76 5.31 57.73 5.66 67.71 5.81 58 59 58.78 5.14 58.75 5.40 58.73 6.66 58.70 6.91 59 60 61 59.77 5.23 59.76 5.49 59.72 5.75 69.70 6.01 60 60.77 5.32 60.74 6.58 60.72 5.85 60.69 6.11 61 62 61.76 5.40 61.74 5.67 61.71 5.94 61.69 6.21 62 63 62.76 6.49 62.74 5.76 62.71 6.04 62.68 6.31 63 64 63.76 5.58 63.73 5.86 63.71 6.13 63.68 6.41 64 65 64.75 5.67 64.73 5.95 64.70 6.23 64.67 6.51 65 66 65.75 5.75 65.72 6.04 66.70 6.33 65.67 6.61 66 67 66.75 5.84 66.72 6.13 66.69 6.42 66.66 6.71 67 68 67.74 5.93 67.71 6.22 67.69 6.62 67.66 6.81 68 69 68.74 6.01 68.71 6.31 68.68 6.61 68.65 6.91 69 70 71 69.73 70.73 6.10 69.71 6.41 69.68 6.71 69.65 7.01 70 71 6.19 70.70 6.50 70.67 6.81 70.64 7.11 72 71.73 6.28 71.70 6.59 71.67 6.90 71.64 7.21 72 73 72.72 6.36 72.69 6.68 72.66 7.00 72.63 7.31 73 74 73.72 6.45 73.69 6.77 73.66 7.09 73.63 7.41 74 75 74.71 6.54 74.69 6.86 74.65 7.19 74.62 7.51 75 76 75.71 6.62 75.68 6.95 76.65 7.28 75.62 7.61 76 77 76.71 6.71 76.68 7.05 76.65 7.38 76.61 7.71 77 78 77.70 6.80 77.67 7.14 77.64 7.48 77.61 7.81 78 79 78.70 6.89 78.67 7.23 78.64 7.57 78.60 7.91 79 80 81 79.70 80.69 6.97 79.66 7.32 79.63 7.67 79.60 8.02 80 81 7.06 80.66 7.41 80.63 7.76 80.59 8.12 82 83 81.69 7.15 81.66 7". 50 81.62 7.86 81.59 8.22 82 82.68 7.23 82.65 7.59 82.62 7.96 82.58 8.32 83 84 83.68 7.32 83.65 7.69 83.61 8.05 83.58 8.42 84 85 84.68 7.41 84.64 7.78 84.61 8.16 84.67 8.52 85 86 85.67 7.50 85.64 7.87 86.60 8.24 85.57 8.62 86 87 86.67 7.58 86.64 7.96 86.60 8.34 86.66 8.72 87 88 87.67 7.67 87.63 8.06 87.59 8.43 87.66 8.82 88 89 88.66 7.76 88.63 8.14 88.59 8.63 88.65 8.92 89 90 91 89.66 7.84 89.62 8.24 89.59 8.63 89.55 9.02 90 90.65 7.93 90.62 8.33 90.58 8.72 90.54 9.12 91 92 91.65 8.02 91.61 8.42 91.68 8.82 91.54 9.22 92 93 92.65 8.11 92.61 8.51 92.57 8.91 92.53 9.32 93 ■ 94 93.64 8.19 93.61 8.60 93.57 9.01 93.63 9.42 94 95 94.64 8.28 94.60 8.69 94.56 9.11 94.52 9.62 95 96 95.63 8.37 95.60 8.78 96.66 9.20 95.52 9.62 96 97 96.63 8.45 96.59 8.88 96.55 9.30 96.51 9.72, 97 98 97.63 8.54 97.59 8.97 97.56 9.39 97.51 9.82 98 . 99 98.62 8.63 98.59 9.06 98.54 9.49 98.50 9.92 99 100 99.62 8.72 99.58 9.15 99.54 9.58 99.50 10.02 100 s Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i 85 r )eg. 84J Deg. 84| Deg. 84i Deg. » 14 TRAVERSE TABLE. 6 Deg. 6\ Deg. H Deg. 61 Deg. 55 o i Lat. Dep. Lat. 1 Dep. Lat. Dep. Lat. 0.99 Dep. 1 0.99 0.101 0.99 0.11 1 0.99 0.11 0.12 1 2 1.99 0.21 1.99 0.22 1.99 0.23 1.99 0.24 2 3 2.98 0.31 2.98 0.33 2.98 0.34 2.98 0.35 3 4 3.98 0.41 3.98 0.44 3.97 0.45 3.97 0.47 4 5 4.97 0.52 4.97 0.54 4.97 0.57 4.97 0.59 5 6 5.97 0.63 5.96 0.65 5.96 0.68 5.96 0.71 6 7 6.96 0.73 6.96 0.76 6.96 0.79 6.95 0.82 7 8 7.96 0.84 7.95 0.87 7.95 0.91 7.94 0.94 8 9 8.95 0.94 8.95 0.98 8.94 1.02 8.94 1.06 9 10 11 9.95 1.05 9.94 1.09 9.94 1.13 9.93 1.18 10 10.94 1.15 10.93 1.20 10.93 1.25 10.92 1.29 11 12 11.93 1.25 11.93 1.31 11.92 1.36 11.92 1.41 12 13 12.93 1.36 12.92 1.42 12.92 1.47 12.91 1.53 13 14 13.92 1.46 13.92 1.52 13.91 1.59 13.90 1.65 14 15 14.92 1.57 14.91 1.63 14.90 1.70 14.90 1.76 15 16 15.91 1.67 15.90 1.74 15.90 1.81 15.89 1.88 16 17 16.91 1.78 16.90 1.85 16.89 1.92 16.88 2.00 17 18 17.90 1.88 17.89 1.96 17.88 2.04 17.88 2.12 18 19 18.90 1.99 18.89 2.07 18.88 2.15 18.87 2.23 19 20 21 19.89 2.09 19.88 20.88 2.18 2.29 19.87 2.26 19.86 2.35 20 20.88 2.20 20.87 2.38 20.85 2.47 21 22 21.88 2.30 21.87 2.40 21.86 2.49 21.85 2.59 22 23 22.87 2.40 22.86 2.50 22.85 2.60 22.84 2.70 23 24 23.87 2.51 23.86 2.61 23.85 2.72 23.83 2.82 24 25 24.86 2.61 24.85 2.72 24.84 2.83 24.83 2.94 25 26 25.86 2.72 25.85 2.83 25.83 2.94 25.82 3.06 26 27 26.85 2.82 26.84 2.94 26.83 3.06 26.81 3.17 27 28 27.85 2.93 27.83 3.05 27.82 3.17 27.81 3.29 28 29 28.84 3.03 28.83 3.16 28.81 3.28 28.80 3.41 29 30 29.84 3.14 29.82 3.27 29.81 3.40 29.79 3.53 30 31 30.83 3.24 30.82 3.37 30.80 3.51 30.79 3.64 31 32 31.82 3.34 31.81 3.48 31.79 3.62 31.78 3.76 32 33 32.82 3.45 32.80 3.59 32.79 3.74 32.77 3.88 33 34 33.81 3.55 33.80 3.70 33.78 3.85 33.76 4.00 34 35 34.81 3.66 34.79 3.81 34.78 3.96 34.76 4.11 35 36 35.80 3.76 35.79 3.92 35.77 4.08 35.75 4.23 36 37 36.80 3.87 36.78 4.03 36.76 4.19 36.75 4.35 37 38 37.79 3.97 37.77 4.14 37.76 4.30 37.74 4.47 38 39 38.79 4.08 38.77 4.25 38.75 4.41 38.73 4.58 39 40 39.78 4.18 39.76 4.35 39.74 4.53 39.72 4.70 40 41 40.78 4.29 40.76 4.46 40.74 4.64 40.72 4.82 41 42 41.77 4.39 41.75 4.57 41.73 4.76 41.71 4.94 42 43 42.76 4.49 42.74 4.68 42.72 4.87 42.70 5.05 43 44 43.76 4.60 43.74 4.79 43.72 4.98 43.70 5.17 44 45 44.75 4.70 44.73 4.90 44.71 5.09 44.69 5.29 45 46 45.75 4.81 45.73 5.01 45.70 5.21 45.68 5.41 46 47 46.74 4.91 46.72 5.12 46.70 5.32 46.67 6.52 47 48 47.74 5.02 47.71 5.23 47.69 5.43 47.67 5.64 48 49 48.73 5.12 48.71 5.34 48.69 5.55 48.66 5.76 49 50 i 49.73 5.23 49.70 5.44 49.68 5.66 49.65 5.88 50 Dep. 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. 0) i 84 Deg. t 831 Deg. B^ Deg. 83i Deg. 5 .2 Q TRAVERSE TABLE. 15 5' g 51 6Deg. 6i Deg. 6i Deg. 6| Deg. 5- 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 50.72 5.33 50.70 5.55 50.67 5.77 50.65 5.99 52 51.72 5.44 51.69 5.66 51.67 5.89 51.64 6.11 52 53 52.71 5.54 52.68 5.77 52.66 6.00 52.63 6.23 53 54 53.70 5.64 53.68 5.88 53.65 6.11 53.63 6.35 54 55 54.70 5.75 54.67 5.99 54.65 6.23 54.62 6.46 55 56 55.69 5.85 55.67 6.10 55.64 6.34 55.61 6.58 56 57 56.69 5.96 56.66 6.21 56.63 6.45 56.60 6.70 57 58 57.68 6.06 57.66 6.31 57.63 6.57 57.60 6.82 58 59 58.68 6.17 58.65 6.42 58.62 6.68 58.59 6.93 59 60 61 59.67 6.27 59.64 6.53 59.61 6.79 69.58 7.05 60 .61 60.67 6.38 60.64 6.64 60.61 6.91 60.58 7.17 62 61.66 6.48 61.63 6.75 61.60 7.02 61.57 7.29 62 63 62.65 6.59 62.63 6.86 62.60 7.13 62.56 7.40 63 64 63.65 6.69 63.62 6.97 63.59 7.25 63.56 7.52 64 65 64.64 6.79 64.61 7.08 64.58 7.36 64.55 7.64 65 66 65.64 6.90 65.61 7.19 65.58 7.47 65.54 7.76 66 67 66.63 7.00 66.60 7.29 66.57 7 58 66.54 7.88 67 68 67.63 7.11 67.60 7.40 67.56 7.70 67.53 7.99 68 69 68.62 7.21 68.59 7.51 68.56 7.81 68.52 8.11 69 70 71 69.62 7.32 69.58 7.62 69.55 7.92 69.51 8.23 70 71 70.61 7.42 70.58 7.73 70.54 8.04 70.51 8.35 72 71.61 7.53 71.57 7.84 71.54 8.15 71.50 8.46 72 73 72.60 7.63 72.57 7.95 72.53 8.26 72.49 8.58 73 74 73.59 7.74 73.56 8.06 73.52 8.38 73.49 8.70 74 75 74.59 7.84 74.55 8.17 74.52 8.49 74.48 8.82 75 76 75.58 7.94 75.55 8.27 75.51 8.60 75.47 8.93 76 77 76.58 8.05 76.54 8.38 76.51 8.72 76.47 9.05 77 78 77.57 8.15 77.54 8.49 77.50 8.83 77.46 9.17 78 79 78.57 8.26 78.53 8.60 78.49 8.94 78.45 9.29 79 80 81 79.56 8.36 79.53 8.71 79.49 9.06 79.45 9.40 80 81 80.56 8.47 80.52 8.82 80.48 9.17 180.44 9.52 82 81.55 8.57 81.51 8.93 81.47 9.28 81.43 9.64 82 83 82.55 8.68 82.51 9.04 82.47 9.40 82.42 9.76 83 84 83.54 8.78 83.50 9.14 83.46 9.51 83.42 9.87 84 85 84.53 8.88 84.50 9.25 84.45 9.62 84.41 9.99 85 86 85.53 8.99 85.49 9.36 85.45 9.74 85.40 10.11 86 87 86.52 9.09 86.48 9.47 86.44 9.85 86.40 10.23 87 88 87.52 9.20 87.48 9.58 87.43 9.96 87.39 10.34 88 89 88.51 9.30 88.47 9.69 88.43 10.08 188.38 10.46 89 90 91 89.51 9.41 89.47 9.80 89.42 10.19 89.38 10.58 90 91 90.50 9.51 90.46 9.91 90.42 10.30 90.37 10.70 92 91.50 9.62 91.45 10.02 91.41 10.41 91.36 10.81 92 93 92.49 9.72 92.45 10.12 92.40 10.53 92.36 10.93 93 94 93.49 9.83 93.44 10.23 93.40 10.64 93.35 11.05 94 95 94.48 9.93 94.44 10.34 94.39 10.75 94.34 11.17 95 96 95.47 10.03 95.43 10.45 95.38 10.87 95.33 11.28 96 97 96.47 10.14 96.42 10.56 96.38 10.98 96.33 11.40 97 98 97.46 10.24 97.42 10.67 97.37 11.09 97.32 11.52 98 99 98.46 10.35 98.41 10.78 98.36 11.21 98.31 11.64 99 100 6 o § .2 99.45 10.45 99.41 10.89 99.36 11.32 99.31 11.75 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Latr 84 Deg. 831 Deg. s^ Deg. 83i Deg. 36 TRAVERSE TAELfi. GB 1 1 7Deg. n Deg. n Deg. 71 Deg. p 1 Lat. Dep. Lat. Dep. Lat Dep. Lat. Dep. 0.99 0.12 0.99 0.13 1 0.99 0.13 0.99 0.13 I 2 1.99 0.24 1.98 0.25 1.98 0.26 1.98 0.27 2 3 2.98 0.37 2.98 0.38 2.97 0.39 2.97 0.40 3 4 3.97 0.49 3.97 0.50 3.97 0.52 3.96 0.54 4 5 4.96 0.61 4.96 0.63 4.96 0.65 4.95 0.67 5 6 5.96 0.73 5.95 0.76 5.95 0.78 5.95 0.81 6 ' 7 6.95 0.85 G.94 0.88 6.94 0.91 6.94 0.94 7 8 7.94 0.97 7.94 1.01 7.93 1.04 7.93 1.08 8 9 8.93 1.10 8.93 1.14 8.92 1.17 8.92 1.21 9 10 TT 9.93 1.22 9.92 1.26 1.39 9.91 1.31 9.91 1.35 1.48 10 11 10.92 1.34 10.91 10.91 1.44 10.90 12 11.91 1.46 11.90 1.51 11.90 1.57 11.89 1.62 12 13 12.90 1.58 12.90 1.64 12.89 1.70 12.88 1.75 13 14 13.90 1.71 13.89 1.77 13.88 1.83 13.87 1.89 14 15 14.89 1.83 14.88 1.89 14.87 1.96 14.86 2.02 15 16 15.88 1.95 15.87 2.02 15.86 2.09 15.85 2.16 16 17 16.87 2.07 16.86 2.15 16.85 2.22 16.84 2.29 17 18 17.87 2.19 17.86 2.27 17.85 2.35 17.84 2.43 18 19 18.86 2.32 18.85 2.40 18.84 2.48 18.83 2.56 19 20 21 19.85 2.44 19.84 2.52 19.83 2.61 19.82 2.70 20 21 20.84 2.56 20.83 2.65 20.82 2.74 20.81 2.83 22 21.84 2.68 21.82 2.78 21.81 2.87 21.80 2.97 22 23 22.83 2.80 22.82 2.90 22.80 3.00 22.79 3.10 23 24 23.82 2.92 23.81 3.03 23.79 3.13 23.78 3.24 24 25 24.81 3.05 24.80 3.15 24.79 3.26 24.77 3.37 25 26 25.81 8.17 25.79 3.28 25.78 3.39 i 25.76 3.51 26 27 26.80 3.29 26.78 3.41 26.77 3.52 26.75 3.64 27 28 27.79 3.41 27.78 3.53 27.76 3.65 27.74 3.78 28 29 28.78 3.53 28.77 3.66 28.75 3.79 28.74 3.91 29 30 31 29.78 3.66 29.76 3.79 29 . 74 3.92 29.73 4.05 30 30.77 3.78 30.75 3.91 30.73 4.05 30.72 4.18 3i 32 31.76 3.90 31.74 4.04 31.73 4.18 31.71 4.32 32 33 32.75 4.02 32.74 4.16 32.72 4.31 32.70 4.45 33 34 33.75 4.14 33. 73 4.29 33.71 4.44 33.69 4.58 34 35 34.74 4.27 34.72 4.42 34.70 4.57 34.68 4.72 35 36 35.73 4.39 35.71 4.54 35.69 4.70 35.67 4.85 36 37 36.72 4.51 36.70 4.67 36.68 4.83 36.66 4.99 37 38 37.72 4.63 37.70 4.80 37.67 4.96 37.65 5.12 38 39 38.71 4.75 38.69 4.92 38.67 5.09 38.64 5.26 39 40 41 39.70 4.87 39.68 40.67 5.05 39.66 5.22 39.63 5.39 40 41 40.70 5.00 5.17 40.65 5.35 40.63 5.53 42 41.69 5.12 41.66 5.30 41.64 5.48 41.62 5.66 42 43 42.68 5.24 42.66 5.43 42.63 5.61 42.61 5.80 43 44 48.67 5.36 43.65 5.55 43.62 5.74 43.60 5.93 44 45 44.67 5.48 44.64 5.68 44.62 5.87 44.59 6.07 45 46 45.66 5.61 45.63 5.81 45.61 6,00 45.58 6.20 46 47 46.65 5.73 46.62 5.93 46.60 6.13 46.57 6.34 47 48 47.64 5.85 47.62 6.06 47.59 6.27 47.. 56 6.47 48 49 48.63 5.97 48.61 6.18 48.58 6.40 48.55 6.61 49 50 J .2 49.63 6.09 49.60 6.31 49.57 6.53 49.54 6.74 50 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 6 o c d Q 83 1 )eg. 821 ] 3eg. . 821 Deg. 82i Deg. TKAVERSE TABLE. n i s 51 7Deg. 1\ ^^g. 1 1^ Deg. 7J Deg. i 51 Lat. Dep. Lat. Dep. i Lat. Dep. Lat. .50.53 Dep. 50.62 6.22 50.69 6.44 50.56 6.66 6.88 53 51.61 6.34 51.58 6.56 1 51.56 6.79 51.53 7.01 52 53 52.60 6.46 52.58 6.69 52.55 6.92 52.52 7.15 53 54 53.60 6.58 53.57 6.81 53.54 7.05 53.51 7.28 54 55 54.59 6.70 54.56 6.94 54.53 7.18 54.. 50 7.42 55 56 55.58 6.82 55.55 7.07 55.52 7.31 55.49 7.55 56 57 56.58 6.95 1 56.54 7.19 56.51 7.44 56.48 7.69 57 58 57.57 7.07 57.54 7.32 57.50 7.57 57.47 7.82 58 59 58.56 7.19 58.53 7.45 58.50 7.70 58.46 7.96 59 60 61 59.55 7.31 59.52 7.57 59.49 7.83 59.45 8.09 60 61 60.55 7.43 60.51 7.70 60.48 7.96 60. M 8.23 62 61.54 7.56 61.50 7.82 61.47 8.09 61.43 8.36 62 63 62.53 7.68 62.50 7.95 62.46 8.22 •62.42 8.50 63 64 63.52 7.80 63.49 8.08 63.45 8.3a 63.42 8.63 64 65 64.52 7.92 64.48 8.20 64.44 8.48 64.41 8.77 65 ^ 66 65.51 8.04 65.47 8.33 65.44 8.61 65.40 8.90 66 67 66.50 8.17 66.46 8.46 66.43 8.75 66.39 9.04 67 68 67.49 8.29 67.46 8.58 67.42 8.88 67.38 9.17 68 69 68.49 8.41 68.45 8.71 68.41 9.01 68.37 9.30 69 70 71 69.48 8.53 69.44 8.83 69.40 9.14 69.36 9.44 70 71 70.47 8.65 70.43 8.96 70.39 9.27 70.. 35 9.57 72 71.46 8.77 71.42 9.09 71.38 9.40 71.-34 9.71 72 73 72.46 8.90 72.42 9.21 72 38 9.53 72.33 9.84 73 74 73.45 9.02 73.41 9.34 73.37 9.66 73.32 9.98 74 75 74.44 9.14 74.40 9.46 74.36 9.79 74.31 10.11 75 76 75.43 9.26 75.39 9.59 75.35 9.92 75.31 10.25 76 77 76.43 9.38 76.38 9.72 76.34 10.05 76.30 10.38 77 78 77.42 9.51 77. a8 9.84 177.33 10.18 77.29 10.52 78 79 78.41 9.63 78.37 9.97 178.32 10.31 1: 78.28 10.65 79 80 81 79.40 9.75 79.36 10.10 1 79.32 10.44 ii 79.27 10.79 80 81 80.40 9.87 180.35 10.22 80.31 10.57 80.26 10.92 82 81.39 9.99 181.34 10.35 81.30 10.70 81.25 11.06 82 83 82.38 10.12 82.34 10.47 82.29 10.83 82.24 11.19 83 84 83.37 10.24 83.33 10.60 83.28 10.96 83.23 11.33 84 85 84.37 10.36 84.32 10.73 84.27 11.09 84.22 11.46 85 86 85.36 10.48 85.31 10.85 85.26 11.23 85.21 11.60 86 87 86.35 10.60 86.30 10.98 86.26 11.36 86.21 11.73 87 88 87.34 10.72 87.30 11.11 87.25 11.49 87.20 11.87 88 89 88.34 10.85 88.29 11.23 88.24 11.62 88.19 12.00 89 90 ~91 89.33 10.97 89.28 11.36 89.23 11.75 89.18 12.14 90 91 90.32 11.09 90.27 11.48 90.22 11.88 90.17 12.27 92 91.31 11.21 91.26 11.61 91.21 12.01 91.16 12.41 92 93 92.31 11.33 92.26 11.74 92.20 12.14 92.15 12.54 93 94 93.30 11.46 93.25 11.86 93.20 12.27 93.14 12.68 94 95 94.29 11.58 94.24 11.^9 94.19 12.40 94.13 12.81 95 96 95.28 11.70 95.23 12.12 95.18 12.53 95.12 12.95 96 97 96.28 11.82 96.22 12.24 96.17 12.66 96.11 13.08 97 98 97.27 11.94 97.22 12.37 97.16 12.79 97.10 13.22 98 99 98.26 12.07 98.21 12.49 98.15 12.92 98.10 13.35 99 100 u o .2 99.25 12.19 99.20 12.62 99.14 Dep. 13.05 99.09 13.49 100 ! 5 Dep. Lat. Dep. Lat. Lat. Dep. Lat. 83 Deg. 82| Deg. 82i Deg. 82i Deg. 18 TRAVERSE TABLE. g 8 Deg. 1 8i Deg. 8|] Deg. 8| Deg. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.99 0.14 0.99 0.14 0.99 0.15 0.99 0.15 1 2 1.98 0.28 1.98 0.29 1.98 0.30 1.98 0.30 2 3 2.97 0.42 2.97 0.43 2.97 0.44 2.97 0.46 3 4 3.96 0.56 3.96 0.57 3.96 0.59 3.95 0.61 4 5 4.95 0.70 4.95 0.72 4.95 0.74 4.94 0.76 i 5! 6 5.94 0.84 5.94 0.86 5.93 0.89 5.93 0.91 6 7 6.93 0.97 6.93 1.00 6.92 1.03 6.92 1.06 7 8 7.92 1.11 7.92 1.15 7.91 1.18 7.91 1.22 8 9 8.91 1.25 8.91 1.29 8.90 1.33 8.90 1.37 9 10 11 9.90 1.39 9.90 1.43 9.89 1.48 9.88 1.52 1.67 10 11 10.89 1.53 ;0.89 1.58 10.88 1.63 10.87 12 11.88 1.67 11.88 1.72 11.87 1.77 11.86 1.83 12 13 12.87 1.81- 12.87 1.87 12.86 1.92 12.85 1.98 13 14 13.86 1.95 13.86 2.01 13.85 2.07 13.84 2.13 14 15 14.85 2.09 14.85 2.15 14.84 2.22 14.83 2.28 15 16 15.84 2.23 15.84 2.30 15.82 2.36 15.81 2.43 16 17 16.83 2.37 16.83 2.44 16.81 2.51 16.80 2.59 17 18 17.82 2.51 17.81 2.58 17.80 2.66 17.79 2.74 18 19 18.82 2.64 18.80 2.73 18.79 2.81 18.78 2.89 19 20 21 19.81 2.78 19.79 2.87 19.78 2.96 19.77 3.04 20 20.80 2.92 20.78 3.01 20.77 3.10 20.76 3.19 21 22 21.79 3.06 21.77 3.16 21.76 3.25 21.74 3.35 22 23 22.78 3.20 22.76 3.30 22,75 3.40 22.73 3.50 23 24 23.77 3.34 23.75 3.44 23.74 3.55 23.72 3.65 24 25 24.76 3.48 24.74 3.59' 24.73 3.70 1 24.71 3.80 25. 26 25.75 3.62 25.73 3.73 25.71 3.84 125.70 3.96 26 27 26.74 3.76 26.72 3.87 26.70 3.99 126.69 4.11 27 28 27.73 3.90 27.71 4.02 27.69 *4.14 J27.67 4.26 28 29 28.72 4.04 28.70 4.16 28.68 4.29 1 28.66 4.41 29 30 29.71 4.18 29.69 4.30 29.67 4.43 1129.65 4.56 30 31 30.70 4.31 30.68 4.45 30.66 4.58 i'i 30.64 4.72 31 32 31.69 4.45 31.67 4.59 31.65 4.73 i!31.63 4.87 32 33 32.68 4.59 32.66 4.74 32.64 4.88 32.62 5.02 33 34 33.67 4.73 33.65 4.88 33.63 5.03 33.60 5.17 34 35 34.66 4.87 34.64 5.02 34.62 5.17 34.59 5.32 35 36 35.65 5.01 35.63 5.17 35.60 5.. 32 35.58 5.48 38 37 36.64 5.15 36.62 5.31 38.59 5.47 36.57 5.63 37 38 37.63 5.29 37.61 5.45 37.58 5.62 37.56 5.78 38 39 .S8 .62 5.43 38.60 5.60 38.57 5.76 38.55 5.93 39 40 39.61 5.57 39.59 5.74 39.56 5.91 39 . 53 6.08 40 41 40.60 5.71 40.58 5.88 40.55 6.06 40.52 6.24 41 42 41.59 5.85 41.57 6.03 41.. 54 6.21 41.51 6.39 42 43 42.. 58 5.98 42.56 6.17 42.53 6.36 42.50 6.54 43 44 43.57 6.12 43.54 6.31 43.52 6.50 43.49 6.69 44 45 44.56 6.26 44.53 6.46 44.51 6.65 44.48 6.85 45 46 45.55 6.40 45.52 -6.60 45.49 6.80 1 45.46 7.00 46 47 46.54 6.54 46.51 6.74 46.48 6.95 46.45 7.15 47 • 48 47.53 6.68 47.50 6.89 47.47 7.09! 47.44 7.30 48 49 48.52 6.82 48.49 7.03 48.46 7.24!! 48.43 7.45 49 ^0 49.51 6.98 49.48 7.17 49.45 7.39 1! 49.42 7.61 50 1 Dep. Lat. Dep. Lat. Dep. Lat. 1 1 Dep Lat. C3 1 .22 P 82 1 )eg 811 Deg. 8U- 1 Deg. 1 81J ] Oeg. TJKAVERSE TABLE. 19 s ~5T 8 Deg. n\ Deg. H Deg. 81 Deg. 5 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 50.50 7.10 50.47 7.32 50.44 7.54 i 50.41 7.76 52 51.49 7.24 51.46 7.46 51.43 7.69 1 51.39 7.91 52 53 52.48 7.38 52.45 7.61 52.42 7.83 52.38 8.06 53 54 53.47 7.52 53.44 7.75 53.41 7.98 53.37 8.21 54 55 54.46 7.65 54.43 7.89 54.40 8.13 54.36 8.37 55 56 55.46 7.79 55.42 8.04 55.38 8.28 55.35 8.52 56 57 56.45 7.93 .56.41 8.18 56.37 8.43 56.34 8.67 57 58 57.44 8.07 57.40 8.32 57.36 8.57 57.32 8.82 58 59 58.43 8.21 58.39 8.47 58.35 8.72 58.31 8.98 59 60 61 59.42 8.35 .59.38 8.61 59.34 8.87 59.30 9.13 60 61 60.41 8.49 60.37 8.75 60.33 9.02 60.29 9.28 62 61.40 8.63 61.36 8.90 61.32 9.16 61.28 9.43 62 63 62.39 8.77 62.35 9.04 62.31 9.31 62.27 9.58 63 64 63.38 8.91 63.34 9.18 63.30 9.46 63.26 9.74 64 65 64.37 9.05 64.33 9.33 64.29 9.61 64.24 9.89 65 66 65.36 9.19 65.32 9.47 65.28 9.76 65.23 10.04 66 67 66.35 9.32 66.31 9.61 66.26 9.90 66.22 10.19 67 68 67.34 9.46 67.30 9.76 67.25 10.05 1 67.21 10.34 68 69 68.33 9.60 68.29 9.90 68.24 10.20 68.20 10.50 69 70 71 69.32 9.74 69.28 10.04 69.23 10.35 69.19 10.65 70 71 70.31 9.88 70.27 10.19 70.22 10.49 70.17 10.80 72 71.30 10.02 71.25 10.33 71.21 10.64 71.16 10.95 72 73 72.29 10.16 72.24 10.47 72.20 10.79 72.15 11.10 73 74 73.28 10.30 73.23 10.62 73.19 10.94' 73.14 11.26 74 75 74.27 10.44 74.22 10.76 74.18 11.09 74.13 11.41 75 76 75.26 10.58 75.21 10.91 75.17 11.23 75.12 11.56 76 77 76.25 10.72 76.20 11.05 76.15 11.38 70.10 11.71 77 78 77.24 10.86 77.19 11.19 77.14 11.53 77.09 11.87 78 79 78.23 10.99 78.18 11.34 78.13 11.68 78.08 12.02 79 80 81 79.22 11.13 79.17 11.48 79.12 80.11 11.82 '11.97' 79.07 12.17 12.32 SO 81 80.21 11.27 80.16 11.62 80.06 82 81.20 11.41 81.15 11.77 81.10 12.12 81.05 12.47 82 83 82.19 11.55 82.14 11.91 82.09 12.27 82.03 12.63 83 84 83.18 11.69 83.13 12.05 83.03 12.42 83.02 12.78 84 85 84.17 11.83 84.12 12.20 84.07 12.56 84.01 12.93 85 86 85.16 11.97 85.11 12.34 85.06 12.71 85.00 13.08 86 87 86.15 12.11 86.10 12.48 86.04 12.86 85.99 13.23 87 88 87.14 12.25 {87.09 12.63 87.03 13.01 86.98 13.39 88 89 88.13 12.39 88.08 12.77 88.02 13.16 87.96 13.54 89 90 91 89.12 12.53 89.07 90.06 12.91 89.01 13.30 88.95 89.94 13.69 90 91 90.11 12.66 13.06 90.00 13.45 13.84 93 91.10 12.80 91.05 13.20 90.99 13.60 90.93 14.00 93 92.09 12.94 92.04 13.34 91.98 13.75 91.92 14.15 93 94 93.09 13.08 93.03 13.49 92.97 13.89 92.91 14.30 94 95 94.08 13.22 94.02 13.63 93.96 14.04 93.89 14.45 95 96 95.07 13.36 95.01 13.78 94.95 14.19 94.88 14.60 96 97 93.06 13.50 96.00 1 96.99 13.92 95.93 14.34 95.87 14.76 97 93 97.05 13.64 14.06 96.92 14.49 96.86 14.91 98 99 98.04 13.78 ! 97.98 14.21 97.91 14.63 97.85 15.06 99 100 8 1 99.03 13.92 1 98.97 14.35 98.90 14.78 98.84 15.21 100 6 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 82 Deg. 01 i Deg. 81i Deg. 8U Deg. 20 TRAVKliSE TABLE- o CD 9De^. n Deg. H Deo-. 9.1 Deg. C 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.99 0.16 0.99 0.16 0.99 0.17 0.99 0.17 2 1.98 0.31 1.97 0.32 1.97 0.33 1.97 0.34 2 3 2.96 0.47 2.96 0.48 2.96 0.50 2.96 0.51 3 4 3.95 0.63 3.95 0.64 3.95 0.66 3.94 0.68 4 5 4.94 0.78 4.93 0.80 4.93 0.83 4.93 0.85 5 6 5.93 0.94 5.92 0.96 5.92 0.99 5.91 1.02 6 7 6.91 1.10 6.91 1.13 6.90 1.16 6.90 1.19 7 8 7.90 1.25 7.90 1.29 7.89 1.32 7.88 1.35 8 9 8.89 1.41 8.88 1.45 8.88 1.49 8.87 1.52 9 10 11 9.88 1.56 9.87 1.61 9.86 1.65 9.86 1.69 10 11 10.86 1.72 10.86 1.77 10.85 1.82 10.84 1.86 12 11.85 1.88 11.84 1.93 11.84 1.98 11.83 2.03 12 13 12.84 2.03 12.83 2.09 12.82 2.15 12.81 2.20 13 14 13.83 2.19 13.82 2.25 13.81 2.31 13.80 2.37 14 15 14.82 2.35 14.80 2.41 14.79 2.48 14.78 2.54 15 16 15.80 2.50 15.79 2.57 15.78 2.64 15.77 2.71 16 17 16.79 2.66 16.78 2.73 16.77 2.81 16.75 2.88 17 18 17.78 2.82 17.77 2.89 17.75 2.97 17.74 3.05 18 19 18.77 2.97 18.75 3.05 18.74 3.14 18.73 3.22 19 20 21 19.75 3.13 19.74 3.21 3.38 19.73 3.30 19.71 3.39 20 20.74 3.29 20.73 20.71 3.47 20.70 3.56 21 22 21.73 3.44 21.71 3.54 21.70 3.63 21.68 3.73 22 23 22.72 3.60 22.70 3.70 22.68 3.80 22.67 3.90 23 24 23.70 3.75 23.69 3.86 23.67 3.96 23.65 4.06 24 25 24.69 3.91 24.67 4.02 24.66 4.13 24.64 4.23 25 26 25.68 4.07 25.66 4.18 25.64 4.29 25.62 4.40 26 27 26.67 4.22 26.65 4.34 26.63 4.46 26.61 4.57 27 28 27.66 4.38 27.64 4.50 27.62 4.62 27.60 4.74 28 29 28.64 4.54 28.62 4.66 28.60 4.79 28.58 4.91 29 30 31 29.63 4.69 29.61 4.82 29.59 4.95 29.57 5.08 30 30.62 4.85 30.60 4.98 30.57 5.12 30.55 5.25 31 32 31.61 5.01 31.58 5.14 31.56 5.28 31.54 5.42 32 33 32.59 5.16 32.57 5.30 32.55 5.45 32.52 5.59 33 34 33.58 5.32 33.56 5.47 33.. 53 5.61 33.51 5.76 34 35 34.57 5.48 34.54 5.63 34.52 5.78 34.49 5.93 35 36 35.56 6.63 35.53 5.79 35.51 5.94 35.48 6.10 36 37 36.54 5.79 36.62 5.95 36.49 6.11 36.47 6.27 37 38 37.53 5.94 37.51 6.11 37.48 6.27 37.45 6.44 38 39 38.52 6.10 38.49 6.27 38.47 6.44 38.44 6.60 39 40 41 39.51 6.26 39.48 6.43 39.45 6.60 6.77 39.42 6.77 40 41 40.50 6.41 40.47 6.59 40.44 40.41 6.94 42 41.48 6.57 41.45 6.75 41.42 6.92 41.39 7.11 42 43 42.47 6.73 42.44 6.91 42.41 7.10 42.38 7.28 43 44 43.46 6.88 43.43 7.07 43.40 7.26 43.36 7.45 44 45 44.45 7.04 44.41 7.23 44.. 38 7.43 44.35 7.62 45 46 45.43 7.20 45.40 7.39 45.37 7.59 45.34 7.79 46 47 46.43 7.35 46.39 7.55 46.36 7.76 46.32 7.96 47 48 47.41 7.51 47.38 7.72 47.34 7.92 47.31 8.13 48 ■ 49 48.40 7.67 48.36 7.88 48.33 8.09 48.29 8.30 49 50 ® 05 49.38 7,82 49.35 8.04 49.32 8.25 49.28 8.47 50 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. s ■ 811 )eg. 801 I )eg. 801 Deg. 801 Deg. teavi::rse tabll;. 21 1 c 9 "51 9 Deg. 9k Deg. H Deg. 91 Deg. S o ? ~51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 Dep. 50.37 7.98 1 50.. 34 8.20 50.30 8.42 50.26 8.64 52 51.36 8.13 51.32 8.36 51.29 8.58 51.25 8.81 52 53 52.35 8.29 52.31 8.52 52.27 8.75 52.23 8.98 53 54 53.34 8.45 1 53.30 8.68 53.26 8.91 53.22 9.14 54 55 54.32 8.60 i 54.28 8.84 54.25 9.08 54.21 9.31 55 56 55.31 8.76 .55.27 9.00 55.23 9.24 55.19 9.48 56 57 56.30 8.92 56.26 9.16 56.22 9.41 56.18 9.65 57 58 57.29 9.07 57.25 ».32 57.20 9.57 57.16 9.82 58 59 58.27 9.23 58.23 9.48 58.19 9.74 58.15 9.99 59 60 61 59.26 9.39 59.22 9.64 59.18 &.90 59.13 10.16 60 61 60.25 9.-54 60.21 9.81 60.16 10.07 60.12 10.33 63 61.24 9.70 61.19 9.97 61.15 10.23 61.10 10.. 50 63 63 62.22 9.86 62.18 10.13 62.14 10.40 62.09 10.67 C3 64 63.21 10.01 63.17 10.29 63.12 10.56 63.08 1 10.84 64 65 64.30 10.17 64.15- 10.45 64.11 10.73 64.06 11.01 65 66 65.19 10.32 65.14 10.61 65.09 10.89 65.05 11.18 66 67 66.18 10.48 66.13 10.77 66.08 11.06 66.03 11.35 67 68 67.16 10.64 67.12 10.93 67.07 11.22 67.02 11.52 68 69 68.15 10.79 68.10 11.09 68.05 11.39 68.00 11.69 69 70 71 69.14 70.13 10.95 11.11 69.09 11.25 69.04 11.55 68.99 11.85 12.02 70 71 70.08 11.41 70.03 11.72 69.97 72 71.11 11.26 71.06 11.57 71.01 11.88 70.96 12.19 72 73 72.10 11.42 72.05 11.73 72.00 12.05 71.95 12.36 73 74 73.09 11.58 73.04 11.89 72.99 12.21 72.93 12.53 74 75 74.08 11.73 74.02 12.06 73.97 12.. 38 73.92 12.70 75 76 75.06 11.89 75.01 12.22 74.96 12.54 174.90 12.87 76 77 76.05 12.05 76.00 12.38 75.94 12.71 '75.89 13.04 77 78 77.04 12.20 76.99 12.54 76.93 12.87 j 76.87 13.21 78 79 78.03 12.36 77.97 12.70 77.92 13.04 77.86 13.38 79 80 81 79.02 12.51 78.96 12.86 13.02 78.90 13.20 78.84 79.83 13.55 13.72 80 81 80.00 12.67 79.95 79.89 13.37 82 80.99 12.83 80.93 13.18 80.88 13.53 180.82 13.-89 82 S'4 81.98 12.98 81.92 13.34 81.86 13.70 81.80 14.06 83 84 82.97 13.14 82.91 13.50 82.85 13.86 ; 82.79 14.23 84 85 83.95 13.30 83.89 13.66 83.83 14.03 183.77 14.39 85 86 84.94 13.45 84.88 13.82 84.82 14.19 184.76 14.56 86 87 85.93 13.61 85.87 13.98 85.81 14.36 85.74 14.73 87 88 86.92 13.77 86.86 14.15 186.79 14.. 52 '86.73 14.90 88 89 87.90 13.92 87.84 14.31 187.78 14.69 187.71 15.07 89 90 91 88.89 14.08 88.83 89.82 14.47 14.63 1 88.77 14.85 188.70 15.24 90 91 89.88 14.24 89.75 15.02 189.69 15.41 92 90.87 14.39 90.80 14.79 90.74 15.18 90.67 15.58 92 93 91.86 14.55 91.79 14.95 91.72 15.35 91.66 15.75 93 94 92.84 14.70 92.78 15.11 92.71 15.51 92.64 15.92 94 95 93.83 14.86 93.76 15.27 93.70 15.68 93.63 16.09 95 96 94.82 15.02 94.75 15.43 94.68 15.84 94.61 16.26 96 97 95.81 15.17 95.74 15.59 95.67 16.01 96.60 16.43 97 . 98 96.79 15.33 96.73 15.75 96.66 16.17 96.58 16.60 98 99 1 97.78 15.49 97.71 15.91 97.64 16.34 97.57 16.77 99 100 i a w Q 198.77 15.64 98.70 16.07 98.63 16.50 98.56 16.93 100 c ei Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 81 Deg. 801 Deg. ■ 80i Deg. iBAVEiJSi: TA'iiLE. o 5' . g P 1 10 Deg. m Deg. Ij m Deg. 101 Deg. 5' s o o i Lat. Dep. \ Lat. Dep. 1 Lat. Dep. Lat. Dep. ! 0.98 0.17 0.98 0.18 0.98 0.18 0.98 0.19 2 ! 1.97 0.35 1.97 0.36 1.97 0.36 1.96 0..37 2 3 j 2.95 0.52 2.95 0.53 2.95 0.55 2.95 0..56 3 4 ! 3.94 0.69 3.94 0.71 3.93 0.73 3.93 0.75 4 5 ! 4.92 0.87 4.92 I 0.89 4.92 0,91 4.91 0.93 5 6 j 5.91 1.04 5.90 1 1.07 5.90 1.09 5.89 1.12 6 7 6.89 1.22 6.89 1.25 6.88 1.28 6.88 1.31 7 8 ' 7.88 1.39 7.87 1.42 7.87 1.46 7.86 1.49 8 9 8.86 1.56 8.86 1.60 8.85 1.64 8.84 1.68 9 10 11 9.85 10.83 1.74 1.01 9.84 1.78 9.83 1.82 9.82 1.87 10 11 10.82 1.96 10.82 2.00 10.81 2.05 12 11.82 2.08 11.81 2.14 11.80 2.19 11.79 2.24 ^9, IS 12.80 2.26 12.79 2.31 12.78 2.37 12.77 2.42 13 14 13.79 2.43 13.78 2.49 13.77 2.55 13.75 2.61 14 15 14.77 2.60 14.76 2.67 14.75 2.73 14.74 2.80 15 m 15.76 2.78 15.74 2.85 15.73 2.92 15.72 2.98 16 17 16.74 2.95 16.73 3.03 16.72 3.10 16.70 3.17 17 18 17.73 3.13 lV.71 3.20 17.70 3.28 17.68 3.36 18 19 18.71 3.30 18.70 3.38 18.68 3.46 18.67 3.54 19 20 21 19.70 3.47 19.68 3.56 19.67 3.64 19.65 3.73 20 21 20.68 3.65 20.66 3.74, 20.65 3.83 20.63 3.92 22 21.67 3.82 21.65 3.91 21.63 4.01 21.61 4.10 22 23 22.65 3.99 j 4.17 22.63 4.09 i 22.61 4.19 22.60 4.29 23 24 23.64 .23.62 4.27 i 23.60 4.37 23.58 4.48 24 25 24.62 4.34 ' 24.60 4.45 i 24.58 4.56 24.56 4.66 25 26 25.61 4.51 25.59 4.63 j 25.56 4.74 25.54 4.85 26 27 26.59 4.69 26.57 4.80 26.55 4.92 26.53 5.04 27 28 27.57 4.86 27.55 4.98 27.53 5.10 27.51 5.22 28] 29 28.56 5.04 28.54 5.16 28.51 5.28 28.49 5.41 29 30 31 29.54 5.21 29.52 5.34 29.50 5.47 29.47 5.60 30 31 30.53 5.38 30.51 5.52i 30.4-8 5.65 30.46 5.78 32 31.51 5.56 31.49 5.69 31.46 5.83 31.44 5.97 32 33 32.50 5.73 32.47 5.87 32.45 6.01 32.42 6.16 33 34 33.48 5.90 33.46 6.05 33.43 6.20 33.40 6.34 34 35 34.47 6.08 34.44 6.23 34.41 6.38 34.39 6.53 ,35 36 35.45 6.25 35.43 6.411 35.40 6.56 35.37 6.71 36 37 36.44 6-42 36.41 6.58 36.38 6.74 36.35 6.90 37 38 37.42 6.60 37.39 6.76 1 37.36 6.92 37.33 7.09 38 39 38.41 6.77 38.38 6.941 38.35 7.11 38.32 7.27 39 40 41 39.39 6.95 39.36 7.12i 39.33 7.29 39.30 7.46 40 41 40.38 7.12 40.35 7.30 1 40.31 7.47 40.28 7.65 42 41.36 7.29 41.33 7.47 1 41.30 7.65 41.26 7.83 42 43 42.35 7.47 42.31 7.65 42.28 7.84 42.25 8.92 43 44 43.33 7.64 43.30 7.83 43.26 8.02 43.23 8.21 U 45 44.32 7.-81 44.28 8.01 44.25 8.20 44.21 8.39 45 46 45.30 7.99 45.27 8.191 45.23 8.38 45.19 8,58 46 47 46.29 8.16 46.25 8.36 46.21 8.57 46.18 8.77 47 48 47.27 8.34 -47.23 8.54 47.20 8.75 47.16 8.95 48 49 48.26 8.51 48.22 8.72 48.18 8.93 48.14 9.14 49 _50 • § 49.24 8.68 49.20 8.90 49.16 9.11 49.12 9.33 50 o o a ej Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 801 3eg. 79i Deg. •791 Deg. 7941 Deg. TRAVERSE TABLE. 2S o 1 ? 51 10 Deg. 1 lOi Deg. lOi Deg. 10| Deg. D 60 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 50.23 8.86 50.19 9.08 50.15 9.29 .50.10 9.51 52 51.21 9.03 51.17 9.25 51.13 9.48 51.09 9.70 52 53 52.19 9.20 52.15 9.43 .52.11 9.66 52.07 9.89 53 54 53.18 9.38 53.14 9.61 53.10 9.84 53.05 10.07 54 55 54.16 9.55 54.12 9.79 54.08 10.02 54.03 10.26 55 50 55.15 9.72 55.11 9.96 55.06 10.21 55.02 10.45 56 57 56.13 9.90 I 56.09 10.14 56.05 10.39 56.00 10.63 57 58 57.12 10.07 57.07 10.32 57.03 10.57 56.98 10.82 58 59 58.10 10,25 58.06 10.50 58.01 10.75 57.96 11.00 59 60 61 59.09 10.42 59.04 10.68 59.00 10.93 58.95 11.19 60 60.07 10.59 60.03 10.85 59.98 11.12 59.93 11.38 61 62 61.06 10.77 61.01 11.03 60.96 11.30 60.91 11.56 62 63 62.04 10.94 61.99 11.21 61.95 11.48 61.89 11.75 63 61 63.03 11.11 62.98 11.39 62.93 11.66 62.88 11.94 64 65 64.01 11.29! 63.96 11.57 63.91 11.85 63.86 12.12 65 66 65.00 11.46 64.95 11.74 64.89 12.03 64.84 12.31 66 67 65.98 11.63 65.93 11.92 65.88 12.21 65.82 12.50 67 68 66.97 11.81 66.91 12.10 66.86 12.39 66.81 12.68 68 69 67.95 11.98 67.90 12.28 67.84 12.57 67.79 12.87 69 70 71 68.94 12.16 68.88 12.46 68.83 12.76 68.77 13.06 _70 71 69.92 12.33 69.87 12.63 69.81 12.94 69.75 13.24 72 70.91 12.50 70.85 12.81 70.79 13.12 70.74 13.43 72 73 71.89 12.68 71.83 12.99 71.78 13.30 71.72 13.62 73 74 72.88 12.85 72.82 13.17 72.76 13.49 72.70 13.80 74 75 75 73.86 13.02 73.80 13.35 73.74 13.67 73.68 13.99 76 74.85 13.20 74.79 13.52 74.73 13.85 74.67 14.18 76 77 75.83 13.37 75.77 13.70 75.71 14.03 75.65 14.36 77 78 76.82 13.54 76.76 13.88 76.69 14.21 76.63 14.55 78 79 77.80 13.72 77.74 14.06 77.68 14.40 77.01 14.74 79 80 81 78.78 13.89 78.72 14.24 78.66 14.58 78.60 14.92 80 "81 79.77 14.07 79.71 14.41 79.64 14.76 79.58 15.11 82 80.75 14.24 80.39 14.59 80.63 14.94 80.56 15.29 82 83 81.74 14.41 81.68 14.77 81.61 15.13 81.54 15.48 83 84 82.72 14.59 82.66 14.95 82.59 15.31 82.53 15.67 84 85 83.71 14.76 83.64 15.13 83.58 15.49 83.51 15.85 85 86 84.69 14.93 84.63 15.30 84.56 15.67 84.49 16.04 86 87 85.68 15.11 85.61 15.48 85.. 54 15.85 85.47 16.23 87 88 86.66 15.28 86.60 15.68 86.53 16.04 86.46 16.41 88 89 87.65 15.45 87.. 58 15.84 87.51 16.22 87.44 16.60 89 90 91 88.63 15.63 88.56 16.01 88.49 16.40 88.42 16.79 90 89.62' 15.80 89.55 16.19 89.48 16.58 89.40 16.97 91 92 90.60 15.98 90.53 16.37 90.46 16.77 90.39 17.161 92| 93 91.59 16.15 91.52 16.55 91.44 16.95 91.37 17.35 93 94 92.57 1 16.32 92.50 16.73 92.43 17.13 92.35 17.53 94 95 93.56 116.50 93.48 16.90 93.41 17.31 93.33 17.72 95 96 94.54 1 16.67 94.47 17.08 94.39 17.49 94.32 17.91 96 97 95.53 1 16.84 95.45 1 17.26 95.38 17.68 95.30 18.09 97 98 9G.51 17.02 96.44 17.44 96.36 17.86 96.28 18.28 98 99 97.50 17.19 97.42 17.62 97.34 18.04 97.26 18.47 99 100 i 1 98.48 17.36 98.40 ! 17.79 98.33 18.22 98.25 18.65 Lat. 100 6 o Dep. Lat. Dep. Lat. Dep. Lat. Dep. 80 Deg. 7a| Deg. 79i Deg. 79i Deg. 24- TRAVERSE TABLE, 1 o a 1 11 Deg. m Deg. lli Deg. Ill Deg. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep, 0.98 0.19 0.98 0.20 0.98 0.20 0.98 0.20 1 2 1.96 0.38 1.96 0.39 1 1.96 0.40 1.96 0.41 2 3 2.94 0.57 2.94 0.59 2.94 0.60 2.94 0.61 3 4 3.93 0.76 3.92 0.78 3.92 0.80 3.93 0.82 4 5 4.91 0.95 4.90 0.98 4.90 1.00 4.90 1.02 5 6 5.89 1.14 5.88 1.17 5.88 1.20 5.87 1.22 6 7 6.87 1.34 6.87 1.37 6.86 1.40 6.85 1.43 7 8 7.85 1.53 7.85 1.56 7.84 1.59 7.83 1.63 8 9 8.83 1.72 8.83 1.76 8.82 1.79 8.81 1.83 9 10 n 9.82 1.91 9.81 1.95 9.80 1.99 9.79 2.04 10 10.80 2.10 10.79 2.15 10.78 2.19 10.77 2.24 11 13 11.78 2.29 11.77 2.34 11.76 2.39 11.75 3.44 12 13 12.76 2.48 12.75 3.54 12.74 2.59 12.73 2.65 13 14 13.74 2.67 13.73 2.73 13.72 2.79 13.71 3.85 14 15 14.72 2.86 14.71 2.93 14.70 2.99 14.69 3.06 15 1« 15.71 3.05 15.69 3.12 15.68 3.19 15.66 3.36 16 17 16.69 3.24 16.67 3.32 16.66 3.39 16.64 3.46 17 18 17.67 3.43 17.65 3.51 17.64 3.59 17.62 3.66 18 19 18.65 3.63 18.63 3.71 18.62 3.79 18.60 3.87 19 20 19.63 3.82 19.62 3.90 19.60 3.99 19.58 4.07 20 21 20.61 4.01 20.60 4.10 20.58 4.19 s 4.39 20.. 56 4.38 21 ■ 22 21.60 4.20 21.58 4.29 21.56 21.54 4.48 22 23 22.58 4.39 22.56 4.49 22.54 4.59 22.52 4.68 23 24 23.56 4.58 23.54 4.68 23.52 4.78 1 23.50 4.89 24 25 24.54 4.77 24.53 4.88 24.50 4.98 24.48 5.09 25 26 25.52 4.96 25.50 5.07 25.48 5.18! 25.46 5.30 26 27 26.50 5.15 26.48 5-. 27 26.46 5.38 1 26.43 5.. 50 27 28 27.49 5.34 27.46 5.46 27.44 5.58 27.41 5.70 28 29 38.47 5.53 28.44 5.66 28.42 5.78 28.39 5.91 29 30 31 29.45 5.72 29.42 5.85 29.40 5.98 29.37 6.11 30 30.43 5.92 30.40 6.05 30.38 .6.18 30.35 6.31 31 32 31.41 6.11 31.39 6.24 31.36 6.38 31.33 6.53 32 33 32.39 6.30 32.37 6.44 32.34 6.58 32.31 6.72 33 34 33.38 6.49 33.35 6.63 33.32 6.78 33.29 6.92 34 35 34.36 6.68 34.33 6.83 34.30 6.98 34.27 7.13 35 36 35.34 6.87 35.31 7.02 35.38 7.18 35.25 7.33 36 37 36.33 7.08 36.29 7.22 36.36 7.38 30.22 7.53 37 38 37.30 7.25 37.27 7.41 37.34 7.58 .37.20 7.74 38 ^ 39 38.38 7.44 38.35 7.61 38.33 7.78 38 . 18 7.94 39 40 39.37 7.63 39.33 7.80 39.20 7.97 39.16 8.15 40 41 40.25 7.82 40.21 8.00 40.18 8.17 40.14 8.35 41 42 41.23 8.01 41.19 8.19 41.16 8.37 41 . 12 8.55 42 43 42.31 8.20 42.17 8.39 42.14 8.57 42.10 8.76 43 44 43.19 8.40 43.15 8.. 58 43.12 8.77 43.08 8.96 44 45 44.17 8.59 44.14 8.78 44.10 8.97 44.06 9.16 45 46 45.15 8.78 45.12 8.97 45.08 9^.17 45.04 9.37 46 47 46.14 8.97 46.10 9.17 46.06 9.37 146.02 9.57 47 48 47.12 9.16 47.08 9.36 47.04 9.57 46.99 9.78 48 49 48.10 9.35 48.06 9.56 48.02 9.77 47.97 9.98 49 50 49.08 9.54 49.04 9.75 49.00 9.97 48.95 10.18 50 6 o Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. g .2 Q i 79 Deg. 781 Deg. 'H Deg. 78i Deg. TRAVERSE TA^LE. 11 Deg. lli Deg. Hi Deg. Ill Deg, 5 o a Lat. 1 Dep. Lat. Dep. Lat. Dep. Lat. j Dep. 50.06 1 9.73 50.02 9.95 49.98 10.17 49.93 10.39 ~51 52 51.04! 9.92 51.00 10.14 50.96 10.37 50.91 10.59 52 53 52.03! 10.11 51.98 10.34 51.94 10.57 51.89 10.79 53 54 53.01 i 10.30 52.96 10.. 53 52.92 10.77 52.87 11.00 54 55 53.99 I 10.49 53.94 10.73 53.90 10.97 53.85 11.20 65 56 54.97 10.69 54.92 10.93 54.88 11.16 54.83 11.40 56 57 55.95 10.88 55.90 11.12 55.86 11.36 55.81 11.61 57 58 56.93 11.07 56.89 11.32 56.84 11.56 56. 7S 11.81 58 59 57.92 11.26 57.87 11.51 57.82 11.76 57.76 12.01 59 60 61 58.90 11.45 58.85 11.71 58.80 59.78 11.96 12.16 58.74 12.22 60 59.88 1 11.64 59.83 11.90 59.72 12.42 61 62 60.86 11.83 60.81 12.10 60.76 12.36 60.70 12.63 62 63 61.84 12.02 61.79 12.29 61.74 12.56 61.68 12.83 63 64 62.82 12.21 62.77 12.49 62.72 12.76 62.66 13.03 64 65 63.81 12.40 63.75 12.68 63.70 12.96 63.64 13.24 65 66 64.79 12.59 64.73 12.88 64.68 13.16 64.62 13.44 66 67 65.77 12.78 65.71 13.07 65.66 13.36 65.60 13.64 67 -68 66 . 75 12.98 66.69 13.27 66.63 13.56 66.58 13.85 68 69 67.73 13.17 67.67 13.46 67.61 13.76 67.55 14.05 69 70 71 68.71 13.36 68.66 13.66 6S.59 13.96 68.53 14.25 70 69.70 13.55 69.64 13.85 69.57 14.16 69.51 14.46 71 72 70.68 13.74 70.62 14.05 70.55 14.35 70.49 14.66 72 73 71.66 13.93 71.60 14.24 71.53 14.55 71.47 14.87 73 74 72.64 14.12 72.58 14.44 72.51 14.75 72.45 15.07 74 75 73.62 14.31 73.56 14.63 73.49 14.95 73.43 15.27 75 76 74.60 14.50 74.54 14.83 74.47 15.15 74.41 15.48 76 77 75.59 14.69 75.52 15.02 75.45 15.35 75.39 15.68 77 78 76.57 14.88 76.50 15.22 76.43 15.55 76.37 15.88 78 79 77.55 15.07 77.48 15.41 77.41 15.75 77.34 16.09 79 80 81 78.53 15.26 78.46 15.61 1 78.39 15.95 78.32 16.29 80 79.51 15.46 79.44 15.80 i 79.37 16.15 79.30 16.49 81 82 80.49 15.65 80.42 16.00 i 80.35 16.35 80.28 16.70 82 83 81.48 15.84 81.41 16.19! 81.33 16.55 81.26 16.90 83 84 82.46 16.03 82.39 16.39 82.31 16.75 82.24 17.11 84 85 83.44 16.22 83.37 16.58 83.29 16.95 83.22 17.31 85 86 84.42 16.41 84.35 16.78 84.27 17.15 84.20 17.51 86 87 85.40 16.60 85.33 16.97 85.25 17.35 85.18 17.72 87 88 86.38 16.79 86.31 17.17 86.23 17.54 86.16 17.92 88 89 87.36 16.98 87.29 17.36 87.21 17.74 87.14 18.12 89 90 -91 88.35 17.17 88.27 17.56 j 88.19 17.94 88.11 18.33 90 89.33 17.36 89.25 17.75 89.17 18.14 89.09 18.53 91 '■ 92 90.31 17.55 90.23 17.95 90.15 18.34 90.07 18.74 92 93 91.29 17.75 91.21 18.14 91.13 18.54 91.05 18.94 93 94 92.27 17.94 92.19 18.34! 92.11 18.74 92.03 19.14 94 95 ; 93.25 18.13 93.17 18.53! 93.09 18.94 93,01 19.35 95 96 ' 94.24 18.32 94.16 18.73 i 94.07 19.14 93.99 19.55 96 97! 95.22 18.51 95.14 18.92 i 95.05 19.34 94.97 19.75 97 98 96.20 18.70 96.12 19.13! 96.03 19.54 95.95 19.96 98 99 97.18 18.89 97.10 19.31 jj 97.01 19.74 96.93 20.16 99 100 a « 98.16 Dep. 19.08 98.08 19.51 ! 97.99 19.94 97.90 20.36 100 Lat. Dep. Lat. 1 Dep. Lat. Dep. Lat. 1 .2 Q 79 De^. . 781 Deg. 1 78i] Oeg. 7.8i Deg. 26 TttAVEESE TABLE. p 12 Deg. 124 Deg. 12^ Deg. 12| Deg. 5 i Lat. Dep. Lat. Dep. Lat. 0.98 Dep. Lat. Dep. 1 0.98 0.21 0.98 0.21 0.22 0.98 0.22 1 2 1.96 0.42 1.95 0.42 1.95 0.43 1.95 0.44 2 ;? 2.93 0.62 2.93 0.64 2.93 0.65 2.93 0.66 3 4 3.91 0.83 3.91 0.85 3.91 0.87 3.90 0.88 4 5 4.89 1.04 4.89 1.06 4.88 1.08 4.88 1.10 5 6 5.87 1.25 5.86 1.27 5.86 1.30 5.85 1.32 6 / 6.85 1.46 6.84 1.49 6.83 1.52 6.83 1.54 7 8 7.83 1.66 7.82 1.70 7.81 1.73 7.80 1.77 8 9 8.80 1.87 8.80 1.91 8.79 1.95 8.78 1.99 9 10 11 9.78 2.08 9.77 2.12 9.76 2.16 9.75 2.21 10 10.76 2.29 10.75 2.33 10.74 2.38 10.73 2.43 11 13 11.74 2.49 11.73 2.55 11.72 2.60 11.70 2.65 13 13 12.72 2.70 12.70 2.76 12.69 2.81 12.68 2.87 13 14 13.69 2.91 13.68 2.97 13.67 3.03 13.65 3.09 14 15 14.67 3.12 14.66 3.18 14.64 3.25 14.63 3.31 15 16 15.65 3.33 15.64 3.39 15.62 3.46 15.61 3.53 16 17 16.63 3.53 16.61 3.61 16.60 3.68 16.58 3.75 17 18 17.61 3.74 17.59 3.82 17.57 3.90 17.56 3.97 18 19 18.58 3.95 18.57 4.03 18.55 4.11 18.53 4.19 19 20 21 19.56 4.16 19.54 4.24 19.53 4.33 19.51 4.41 20 20.54 4.37 20.52 4.46 20.50 4.55 20.48 4.63 21 22 21.52 4.57 21.50 4.67 21.48 4.76 21.46 4.86 22 23 22.50 4.78 22.48 4.88 22.45 4.98 22.43 5.08 23 24 23.48 4.99! 23.45 5.09 23.43 5.19 23.41 5.30 24 25 24.45 5.20 i 24.43 5.30 24.41 5.41 24.38 5.52 25 26 25.43 5.41 1 25.41 5.52! 25.38 5.63 25.36 5.74 26 27 26.41 5.61 ; 26.39 5.73! 26.36 5.84 26.33 5.96 27 28 27.39 5.82 27.36 5.94 27.34 6.06 27.31 6.18 28 29 28.37 6.03 28.34 6.15 28.31 6.28 28.28 6.40 29 30 29.34 6.24 29.. 32 6.37 29.29 6.49 29.26 6.62 30 31 30.32 6.45 j 30.29 6.58 30.27 6.71 30.24 6.84 31 32 31.30 6.65 1 31.27 6.79 31.24 6.93 31.21 7.06 32 33 .32.28 6.86! .32.25 7.00 32.22 7.14 32.19 7.28 33 34 .33.26 7.07 33.23 7.21 33.19 7.36 33.16 7.50 34 35 34.24 7.28 34.20 7.43 34.17 7.58 34.14 7.72 35 36 35.21 7.48 35.18 7.64 35.15 7.79 35.11 7.95 36 37 36.19 7.69 36.16 7.85 36.12 8.01 36.09 8.17 37 38. 37.17 7.90 37.13 8.06 37.10 8.22 37.06 8.39 38 39 138.15 8.11 38.11 8.27 38.08 8.44 38.04 8.61 39 40 39.13 8.32 39.09 8.49 39.05 8.66 39.01 8.83 40 41 41 40.10 8.52 40.07 8.70 40.03 8.87 39.99 9.05 42 41. OS 8.73 41.04 8.91 41.00 9.09 40.96 9.27 42 43 42.06 8.94 42.02 9.12 41.98 9.31 41.94 9.49 43 44 43.04 9.15 43.00 9.34 42.96 9.52 42.92 9.71 44 45 44.02 9.36 43.98 9.55 43.93 9.74 43.89 9.93 45 46 44.99 9.56 44.95 9.76 44.91 9.96 44.87 10.15 46 47 45.97 9.77 45.93 9.97 45.89 10.17 45.84 10.37 47 48 46.95 9.98 46.91 10.18 46.86 10.39 46.82 10.59 48 49 47.93 10.19 47.88 10.40 47.84 10.61 47.79 10.81 49 50 48.91 10.40 48.86 10.61 48.81 10.82 48.77 11.03 50 c5 c 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 .3 Q 1 78] ! Deg. 771 Deg. 77^ Deg. 77i Deg. TRAVEHSE TABLE. 2.7 p 61 12 Deg. m DBg. 1 la^Deg. 121 Deg. s P s Lat. Dep. Lat. Dep Lat. Dep. Lat. Dep. 3 9 "51 49.89 10.00 49.84 10.82 49.79 11.04 49.74 11.26 52 50.86 10.81 50.82 11.03 50.77 11.25 50.72 11.48 52 53 51.84 11.02 51.79 11.26 51.74 11.47 61.69 11.70 63 54 52.82 11.23 62.77 11.46 62.72 U.69 62.67 11.92 54 55 53.80 11.44 63.75 11.67 63.70 11.90 53.64 12.14 55 56 54.78 11.64 54.72 11.88 64.67 12.12 54.62 12.36 56 57 55.75 11.85 55.70 12.09 65.65 12.34 56.69 12.58 57 58 56.73 12.06 56.68 12.31 56.63 12.55 56.57 12.80 58 59 57.71 12.27 57.66 12.62 67.60 12.77 57.66 13.02 59 60 61 58.69 12.47 58.63 59.61 12.73 68.68 12.99 58.52 13.24 13.46 60 61 59.67 12.68 12.94 59.56 13.20 59.50 62 60.65 12.89 60.59 13.16 60.63 13.42 60.47 13.68 62 63 61.62 13.10 61.57 13.37 61.51 13.64 61.45 13.90 63 64 62.60 13.31 62.54 13.68 62.48 13.85 62.42 14.12 64 65 63.68 13.61 63.52 13.79 63.46 14.07 63.40 14.35 65 66 64.66 13.72 64.50 14.00 64.44 14.29 64.37 14.67 06 67 65.54 13.93 66.47 14.22 66.41 14.50 66.35 14.79 67 68 66.51 14.14 66.45 14.43 66.39 14.72 66.32 15.01 68 69 67.49 14.35 67.43 14.64 67.36 14.93 67.30 15.23 6£^ 70 71 68.47 14.55 68,41 14.85 68.34 15,15 68.27 15.45 70 69.45 14.76 69.. 38 15.06 69.32 15.37 69.25 15.67 71 72 70.43 14.97 70.36 15.28 70.29 15.58 70.22 15.89 72 73 71.40 16.18 71.34 15.49 71.27 15.80 71.20 16.11 73 74 72.38 15.39 72.32 16.70 72.26 16.02 72.18 16.33 74 75 73.36 15.59 73.29 16.91 73.22 16.23 73.15 16.55 75 76 74.34 15.80 74.27 16.13 74.20 16.46 74.13 16.77 76 77 75.32 16.01 76.25 16.34 75.17 16.67 75.10 16.99 77 78 76.30 16.22 76.22 16.66 76.16 16.88 76.08 17.21 78 79 77.27 16.43 77.20 16.76 77.13 17.10 77.05 17.44 79 '80 81 78.25 16.63 78.18 16.97 17.19 78.10 17.32 78.03 17.66 80 79.23 16.84 79.16 79.08 17.53 79.00 17.88 81 82 80.21 17.06 80.13 17.40 80.06 17.75 79.98 18.10 82 83 81.19 17.26 81.11 17.61 81.03 17.96 80.95 18.32 83 84 82.16 17.46 82.09 17.82 82.01 18.18 81.93 18.54 84 85 83.14 17.67 83.06 18.04 82.99 18.40 82.90 18.76 85„ 86 84.12 17.88 84.04 18.25 83.96 18.61 83.88 18.98 86 87 85.10 18.09 85.02 18.46 84.94 18.83 84.85 19.20 87 88 86.08 18.30 86.00 18.67 85.91 19.06 85.83 19.42 88 89 87.06 18.60 86.97 18.88 86.89 19.26 86.81 19.64 89 90 91 88.03 18.71 87.95 88.93 19.10 87.87 19.48 87.78 19.86 90 89.01 18.92 19.31 88.84 19.70 88.76 20.08 91 92 89.99 19.13 89.91 19.62 89.82 19.91 89.73 20.30 92 93 90.97 19.34 90.88 19.73 90.80 20.13 90.71 20.52 9? 94 91.95 19.64 91.86 19.94 91.77 20.36 91.68 20.75 94 95 92.92 19.75 92.84 20.16 92.75 20.56 92.66 20.97 95 96 93.90 19.96 93.81 20.37 93.72 20.78 93.63 21.19 96 97 94.88 20.17 94.79 20.58 94.70 20.99 94.61 21.41 97 98 95.86 20.38 96.77 20.79 95.68 21.21 96.58 21.63 98 99 96.^4 20.58 96.76 21.01 96.65 21.43 96.56 21.85 99 100 © 5 97.81 20.79 97.72 21.22 97.63 21.64 97.53 22.07 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 78 Deg. 771 D€g 77| Deg. 77i Deg. M ^ THAVERSE TABLE. X-.. p : 13 Deg. I l^i Deg. m Deg. i3J Deg. C Lat. Dep. Lat.! Dep. Lat. Dep. Lat. Dep. 0.97 0.23 0.9? 0.23 0.97 0.23 0.9^ 1 2 1.95 0.4c 1.95 0.46 1.95 0.47 l.r _ 2 3 2.92 0.67 2 . 92 0.69 2.92 0.70 2.-1 3 4' 3.90 0.90 3.^9 0.9-: 3.89 0.93 3.89 0.9.3; 4 5 4.87 1.12 -i . "* 7 1.15 4.86 1.17 4.86 1.19; 5 6 1 5.85 ; 1.35 o!84. 1.3S 5 . 83 1.40 5.83 1.43 6 7 6.82 1.57 6.81 1 1.60 6.81 1.63 1 6.80 1.66 : 7 8 7.80 1.80 7.79 1 1.83 7.78 1.87 ; 7.77: 1.90 8 9 8.77 2.02 8.76 ! 2.06 8.75 2.10 '■ 8.74 2.14 9 10 9.74 2.25 9.73 ! 2.29 9.72 2.33 9.71 2.38 , 10 11 10.72 2.47 10.71 [ 2.. 52 -,, -,-, 2.57 10.68 2.61 11 12 11.69: 2.70 11.68 2.75 ■: . 80 11.66 2.85 ! 12 13 12.67- 2.92 12.65 2.9S 3.03 12.63 3.09 i 13 U 13.64 3.15 13.63 3.21 13.01 3.27 13.60 3.33 14 15 14.62 3.37 14.60 3.44 14.59 3.. 50 14.57 3.57 15 16 15.. 59 3.60 15.57 3.67 1 .' . .5 6 3.74 15.54 3.80 16 17 16.57: 3.82 16.55 3.90 :-' - ^ 1 - ': 1 4.04 17 IS 17. .54; 4.05 17.52 4.i3 -- - ', . 1 -'- ^.28 18 19 IS. 51 4.v;7 18.49 4.35 i?.-±-^ -i . -i-i i ? . -±0 4.52 19 20 19.49 4.. 50 4.72 19.47 4.. 58 1 19.45 20.42 i 4.67 '■ 4.90 19.43 20.40 4.75 4.99 20 21 •M 20.46 20.44 4.81 ; 22 21.44j 4.95 21.41 5.04 2i..39 1 5.14 21.37: 5.23 22 23 22.41 i 5.17 22.39 5.27 ^ 22.36 i 5.37 22.34J 5.47 23 24 23.38 ! 5.40 23.36 5.50 1 23.34 1 5.50 23.31 5.70 1 24 25 24.36 i 5.62 24.33 5.73^ 24.31 ! 5.84 24.28: 5.94! 25 26 25.33 5.85 25.31 5.96 25.28 1 6.07 25.25 6.18; 26 27 26.31 6.07 26.28 6.19 26 . 25 6.30 26.23 6.42 , 27 2v 27.28 6.30 27.25 6.42 27.23 6.. 54 27.20 6.66 28 29 23.26 6.52 2S.23 6.65 28.20 6.77 28.17 6.89 29 30 31 129.23 130.21 6.75 6.97 29.20 6.88 29.17 30.14 7.00 7.24 29.14 30.11 7.13 7.37 30 31 30.17 7.11 32 31.18 7.20 31.15 7.33 31.12 i 7.47 31. OS 7.61 32 33 '32.15 7.42 32.12 7.56 .32.09 7.70 32.05 7 . S4 33 :34 133.13 7.65 33.09 7.79 33.06 ; 7.94 33.03 -H . (") H 34 35 i 34.10 7.87 34.07 8.02 34.03 1 8.17 S.32 35 36 i35.0S 8.10 i 35.04 ; 8.25 35.01 1 8.4) ?..56 36 37 i 36.05 8.32 i 36.02 8.4S 35.98 , 8.64 ■-.'' , .--X ?.79 37 a? 37.03 8.55 * 36.99 e.71 36.95 i 8.87 36.91 9.03 38 39 138.00 8.77 i 37.96 \ 8.94 J 37.92 ' 9.10 37. SS 9.27 39 40 41 ,38.97 139.95 9 . 00 9.22 38.94 39.91 i 9.17 i 9.40 [38.89 .'^9.87 9.34 9.57 3-.^5 9.51 9.75 40 41 3^ , '^3 42 140.92 9.45 40.88 9.63 i 40.84 ^ 9.80 40. Su 9.9S 42 43 ! 41.90 9.67 41.86 ; 9.86 41.81 ■■ 10.04 41.77 10.22 43 44 142.87 9.90 42.83 i 19.08 : 42.7-1 \ 10.27 42 . 74 10.46 44 45 143.85 0.12 43.80 ' iO.31 143.73 10.51 43.71 10.70 45 46 44.82 0.35 , 44.78 • 10. .54 ; 44.73 10.74 44.68 10.93 46 47 45.80 10..: 145.75 1 10.77 '4O.70 10.9- 45.65 11.17 47 4S 46.77 W.80 46.72 11.00 146.67 11.21 46.62 11.41 48 49 47.74 11.02 i 47.70 1 11.23 •47.65 11.44 47.60 11.65 49 50 48.72 11.25 J 48.67 1 11.46 ! 48.62 i Dep. 11.67 Lat. ,i48..57 11.88 50 5 c .2 I Dep. 1 Lat. ! Dep. LaL V Dep. 1 Lat. 1 1 "' Deg. :l '61 Deg. 1 ^^ Deg. ;, 76t li ^ Deg. TRAVERSE TABLE. 29 c 3 9 "51 13 Deg. 13i Deg. 13| Deg. 131 Deg. 1 n 9 Lat. Dep. Lat. Dep. Lat. Dep. Lat Dep. 49.69 11.47 49.64 11.69 49.59 11.91 49.54 12.12 "sI 52 50.67 11.70 50.62 11.92 50.56 12.14 50.51 12.36 52 53 61.64 11.92 51.59 12.15 51.54 12.37 1151.48 12.61 152.45 12.60 53 54 52.62 12.15 52.56 12.38 52.51 12.84 64 55 53.59 12.37 53.54 12.61 53.48 12.84 i .53.42 13.07 55 56 54.66 12.60 54.51 12.84 54.46 13.07 ! 54.40 13.31 56 57 55.54 12.82 55.48 13.06 55.43 13.31 ' 56.37 13.55 57 68 56.51 13.05 56.46 13.29 56.40 13.54: 56.34 13.79 58 59 57.49 13.27 57.43 13.52 57.37 13.77 : 57.31 14.02 59 60 61 58.46 13.50 58.40 13.75 58.34 14.01 14.24 58.28 14.26 60 59.44 13.72 59.38 13.98 59.31 59.25 14.50 61 62 60.41 13.95 60.35 14.21 60.29 14.47 60.22 14.74 62 63 61.39 14.17 61.32 14.44 61.26 14.71 61.19 14.97 63 4 62.36 14.40 62.30 14.67 62.23 14.94 62.17 15.21 64 65 63.33 14.62 63.27 14.90 63.20 16.17 63.14 16.46 65 66 64.31 14.85 64.24 16.13 64.18 15.41 64.11 15.69 66 67 65.28 15.07 65.22 15.36 65.15 15.64 65.08 15.93 67 68 66.26 15.. 30 66.19 16.59 66.12 15.87 66.05 16.16 68 69 67.23 15.. 52 67.16 15.81 67.09 16.11 67. OS 16.40 69 70 71 68.21 15.75 68.14 16.04 16.27 68.07 69.04 10.34 67.99 16.64 70 71 69.18 15.97 69.11 16.57 68.97 16.88 72 70.15 16.20 70.08 16.50 70.01 16.81 69.94 17.11 72 73 71.13 16.42 71.06 16.73 70.98 17.04 70.91 17.35 73 74 72.10 16.65 72.03 16.96 71.96 17.28 71.88 17.59 74 75 73.08 16.87 73.00 17.19 72.93 17.50 72.85 17.83 75 76 74.05 17.10 73.98 17.42 73.90 17.74 73.82 18.06 76 77 75.03 17. .32 74.95 17.65 74.87 17.98 74.79 18.30 77 78 76.00 17.55 75.92 17.88 75.84 1&.21 75.76 18.. 54 78 79 76.98 17.77 76.90 18.11 76.82 18.44 76.74 18.78 79 80 81 77.95 18.00 77.87 78.84 18.34 77.79 18.68 77.71 19.01 80 78.92 18.22 18.57 78.76 18.91 78.68 19.25 81 82 79.90 18.45 79.82 18.79 79.73 19.14 79.65 19.49 82 83 80.87 18.67 80.79 19.02 80.71 19.38 80.62 19.73 83 84 81.85 18.90 81.76 19.25 '81.6.:! 19.61 81.59 19.97 84 85 82.82 19.12 82.74 19.48 '82.65 19.84 82.56 20.20 85 86 83.80 19.35 83.71 19.71 83.62 20.08 83.54 20.44 86 87 84.77 19.57 84.68 19.94 84.60 20.31 84.51 20.68 87 88 85.74 19.80 85.66 20.17 86.67 20 . 54 86.48 20.92 88 89 86.72 20.02 86.63 20.40 i 86.54 20.78 86.45 21.15 89 90 91 87.69 20.25 87.60 88.58 20.63 20.86 87.51 21.01 87.42 21.39 90 88.67 20.47 88.49 21.24 88.39 21.63 9] 92 89.64 20.70 89.55 21.09 89.46 21.48 89.36 21.87 92 93 90.62 20.92 90.52 21.32 90.43 21.71 90.33 22.10 93 94 91.59 21.15 91.50 21.54 91.40 21.94 91.31 22.34 94 95 92.. 57 21.37 92.47 21.77 92.. 38 22. 18 92.28 22.58 95 96 93.54 21.60 93.44 22.00 93.35 22.41 93.25 22.82 96 97 94.51 21.82 94.42 22.23 94.32 22.64 94.22 23.06 97 98 95.49 22.05 95.39 22.46 95.29 22.88 95.19 23.29 98 99 96.46 22.27 96.36 22.69 96.26 23.11 96.16 23.53 99 100 .2 Q 97.44 22.50 97.34 22.92 97.24 23.34 97.13 23.77 ,..;(: Dep. Lat. Dep. Lat. 1 Dep. Lat. Dep. Lat. § c as _ 77 Deaf. 76J Deg. 76A Deg. ■6^ Deg. « 50 TRAVERSE TABLE. 5' P ~~1 14 Deg. 14i Deg. 1 14A Deg. 141 Deg. 1 a 9 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0,97 0.24 0.97 0.25 0.97 0.25 0.97 0.25 2 1.94 0.48 1.94 0.49 1.94 0.50 1.93 0.51 2 3 2.91 0.73 2.91 0.74 5i.90 0.75 2.90 0.76 3 4 3.88 0.97 3.88 0.98 3.87 1.00 3.87 1.02 4 5 4.85 1.21 4.85 1.23 4.84 1.25 4.84 1.27 5 6 5.821 1.45 5.82 1.48 5.81 1.50 5.80 1.53 6 7 6.79' 1.69 6.78 1.72 6.78 1.75 6.77 1.78 7 8 7.76! 1.94 7.75 1.97 7.75 2.00 7.74 2.04 8 9 8.73 i 2.18 8.72 2.22 8.71 2.25 8.70 2.29 9 10 11 9.70' 2.42 9.69 2.46 9.63 2.50 9.67 2.55 10 11 10.67 2.66 10.66 2.71 10.65 2.75 10.64 2.80 12 11.64 2.90 11.63 2.95 11.62 3.00 11.60 3.06 12 13 12.61 3.15 12.60 3.20 12.59 3.25 12.57 3.31 13 14 13.58 3.39 13.57 3.45 13.55 3.51 13.54 3.56 14 15 14.55 3.63 14.54 3.69 14.52 3.76 14.51 3.82 15 16 15.52 3.87 15.51 3.94 15.49 4.01 15.47 4.07 16 17 16.50 4.11 16.48 4.18 1 16.46 4.26 16.44 4.33 17 18 17.47 4.35 17.45 4.43 17.43 4.51 17.41 4.58 18 19 18.44: 4.60 18.42 4.68 1 18.39 4.76 18.37 4.84 19 20 '21 19.41 4.84 19.39 4.-92 1 19.36 20.33 5.01 19.34 5.09 20 21 20.38 5.08 1 20.35 5.17 5.36 20.31 5.35 22 21.35 5.32 21.32 5.42 21.30 5.51 21.28 5.60 22 23 22.32 5.56 22.29 5.68 22.27 5.76 22.24 5.86 23 24 23.99 5.81 23.26 5.91 23.24 6.01 23.21 6.11 24 25 24.26 6.05 24.23 6.15 24.20 6.26 24.18 6.37 25 26 25.23 6.29 25.20 6.40 25.17 6.51 25.14 6.62 26 27 26.20 6.53 26.17 6.65 26.14 6.76 26.11 6.87 27 28 27.17 6.77 27.14 6.89 27.11 7.01 27.08 7.13 28 29 28.14 7.02 28.11 7.14 28.08 7.26 28.04 7.38 29 30 31 29.11 7.26 7.50 29.08 7.38 j 29.04 7.51 29.01 7.64 30 31 30.08 30.05 7.63 30.01 7.76 29.98 7.89 32 31.05 7.74 31.02 7.88 30.98 8.01 30.95 8.15 32 33 32.02 7.98 31.98 8.12 31.95 8.26 31.91 8.40 33 34 32.99 8.23 32.95 8.37 .32.92 8.51 32.88 8.66 34 35 33.96 8.47 33.92 8.62 33.89 8.76 .33.85 8.91 35 36 34.93 8.71 34.89 8.86 34.85 9.01 34.81 9.17 36 37 35.90 8.95 35.86 9.11 35.82 9.26 35.78 9.42 37 38 36.87 9.19 36.83 9.35 36.79 9.51 36.75 9.67 38 39 37.84 9.44 37.80 9.60 37.78 9.76 37.71 9.93 39 40 41 38.81 9.68 38.77 9.85 38.73 10.02 38.68 10.18 40 41 39.78 i 9.^2 39.74 10.09 39.39 10.27 .39.65 10.44 42 40.75 1 10.16 40 71 10.34 40.66 10.52 40.62 10.69 42 43 41.72 i 10.40 41.68 10.58 41.63 10.77 41.58 10.95 43 44 42.69 10.64 42.65 10.83 42.60 11.02 42.55 11.20 44 45 43.66 10.89 43.62 11.08 43.57 11.27 43.52 11.46 45 46 44.63 11.13 44.58 11.32 44.53 11.52 44.48 11.71 46 47 45.60 11.37 45.55 11.57 45.50 11.77 45.45 11.97 47 48 46.57 11.61 46.52 11.82 46.47 12.02 46.42 12.22 48 49 47.54 i 11.85 47.49 12.06 47.44 12.27 47.39 12.48 49 50 o i 48.51 12.10 48.46 12.31 48.41 12.52 48.35 12.73 50 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. ■1 Q 76 Deg. « T5f Deg. 761 Deg. 75i Deg. TRAVEKSE TABLE. 31 p 51 1 14 Deg. 1 14i Deg. 14i Deg. r 14| Deg. ~51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 49.49 12.34 49.43 12.55 49.38 12.77 49.32 12.98 53 50.46 12.58 50.40 12.80 50.34 13.02 50.29 13.24 52 53 51.43 12.82 51.37 13.05 51.31 13.27 51.25 13.49 53 54 52.40 13.06 52.34 13.29 52.28 13.52 52.22 13.75 54 55 53.37 13.31 53.31 13.54 53.25 13.77 53.19 14.00 55 56 .54.34 13.55 54.28 13.78 54.22 14.02 54.15 14.26 56 57 55.31 13.79 55.25 14.03 55.18 14.27 55.12 14.51 57 58 56.28 14.03 56.22 14.28 56.15 14.52 56.09 14.77 58 59 57.25 14.27 57.18 14.52 57.12 14.77 57.06 15.02 59 60 61 58.22 59.19 14.52 58.15 14.77 58.09 15.02 58.02 15.28 60 61 14.76 59.12 15.02 59.06 15.27 58.99 15.53 62 60.16 15.00 60.09 15.26 60.03 15.52 59.96 15.79 62 63 61.13 15.24 61.06 15.51 60.99 15.77 60.92 16.04 63 64 62.10 15.48 62.03 15.75 61.96 16.02 61.89 16.29 64 65 63.07 15.72 63.00 16.00 62.93 16.27 62.86 16.. 55 65 66 64.04 15.97 63.97 16.25 63.90 16.53 63.83 16.80 66 67 65.01 16.21 64.94 16.49 64.87 16.78 64.79 17.06 67 68 65.98 16.45 65.91 16.74 65.83 17.03 65.76 17.31 68 69 66.95 16.69 66.88 16.98 66.80 17.28 66.73 17.57 69 70 71 67.92 16.93 67.85 17.23 67.77 17.53 67.69 17.82 70 71 68.89 17. 1« 17. 4§ 68.82 17.48 68.74 17.78 68.66 18.08 72 69.86 69.78 17.72 69.71 18.03 69.63 18.33 72 73 70.83 17.66 70.75 17.97 70.67 18.28 70.59 18.59 73 74 71.80 17.90 71.72 18.22 71.64 18.53 71.56 18.84 74 75 72.77 18.14 72.69 18.46 72.61 18.78 72.53 19.10 75 76 73.74 18.39 73.66 18.71 73.58 19.03 73.50 19.35 76 77 74.71 18.63 74.63 18.95 74.55 19.28 74.46 19.60 77 78 75.68 18.87 75.60 19.20 75.52 19.53 75.43 19.86 78 79 76.65 19.11 76.57 19.45 76.48 19.78 76.40 20.11 79 80 81 77.62 78.59 19.35 77.54 19.69 77.45 20.03 77.36 78.33 20.37 80 81 19.60 78.51 19.94 78.42 20.28 20.62 82 79.56 19.84 79.48 20.18 79.39 20.53 79.30 20.88 82 83 80.53 20,08 80.45 20.43 80.36 20.78 80.20 21.13 83 84 81.50 20.32 81.42 20.68 81.32 21.03 81.23 21.39 84 85 82.48 20.56 82.38 20.92 82.29 21.28 82.20 21.64 85 86 83.45 20.81 83.35 21.17 83.26 21.53 83.17 21.90 86 87 84.42 21.05 84.32 21.42 84.23 21.78 84.13 22.15 87 88 85.39 21.29 85.29 21.66 85.20 22.03 85.10 22.41 88 89 86.36 21.53 86.26 21.91 86.17 22.28 86.07 22.66 89 90 91 87.33 88.30 21.77 87.23 22.15 87.13 22.. 53 87.03 22.91 23.17 90 91 22.01 88.20 22.40 88.10 22.78 88.00 92 89.27 22.26 89.17 22.65 89.07 23.04 88.97 23.42 92 93 90.24 22.50 90.14 22.89 90.04 23.29 89.94 23.68 93 94 91.21 22.74 91.11 23.14 91.01 23.54 90.90 23.93 94 95 92.18 22.98 92.08 23.38 91.97 23.79 91.87 24.19 96 96 93.15 23.22 93.05 23.63 92.94 24.04 92.84 24.44 96 97 94.12 23.47 94.02 23.88 93.91 24.29 98.80 24.70 97 98 95.09 23.71 94.98 24.12 94.88 24.54 94.77 24.95 98 99 96.06 23 9i» 95.95 24.37 95.85 24.79 95.74 25.21 99 100 6 97.03 24.19 96.92 24.62 96.81 25.04 96.70 25.46 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i 76 Deg. 1 75| Deg. 75i Deg. 75J Deg. h2 TRAVERSE TABLE. P. a a 15 Deg. 15i Deg. 15t Deg. 15| Deg. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.97 0.26 0.96 0.26 0.96 0.27 0.96 0.27 1 2 1.93 0.52 1.93 0.53 1.93 0..53 1.92 0.54 2 3 2.90 0.78 2.89 0.79 2.89 0.80 2.89 0.81 3 4 3.86 1.04 3.86 1.05 3.85 1.07 3.85 1.09 4 5 4.83 1.29 4.82 1.32 4.82 1.34 4.81 1.36 5 6 5.80 1.55 5.79 1.58 5.78 1.60 5.77 1.63 6 7 6.76 1.81 6.75 1.84 6.75 1.87 6.74 1.90 7 8 7.73 2.07 7.72 2.10 7.71 2.14 7.70 2.17 8 9 8.69 2.33 8.68 2.37 8.67 2.41 8.66 2.44 9 10 9.66 2.59 9.65 2.63 9.64 2.67! 9.62 2.71 10 11 10.63 2.85 10.61 2.89 10.60 2.94 10.59 2.99 11 12 11.59 3.11 11.58 3.16 11.56 3.21 11.55 3.26 12 13 12.56 3.36 12.54 3.42 12.53 3.47 1 12.51 3.53 13 14 13.52 3.62 13.51 3.68 13.49 3.74 1 13.47 3.80 14 15 14.49 3.88 14.47 3.95 14.45 4.01 14.44 4.07 15 16 15.45 4.14 15.44 4.21 15.42 4.28 15.40 4.34 16 17 16.42 4.40 16.40 4.47 16.38 4.54 16.36 4.61 17 18 17.39 4.66 17.37 4.73 17.35 4.81 17.32 4.89 18 19 18.35 4.92 18.33 5.00 18.31 5.08 18.29 5.16 19 20 19.32 5.18 19.30 5.26 19.27 5.34 19.25 5.43 20 21 20.28 5.44 20.26 5.52 20.24 5.61 1 20.21 5.70 21 22 21.25 5.69 21.23 5.79 21.20 5.88 21.17 5.97 22 23 22.22 5.95 22.19 6.05 22.16 6.151 22.14 6.24 23 24 23.18 6.21 23.15 6.31 23.13 6.41 ; 23.10 6.51 24 25 24.15 6.47 24.12 6.. 58 24.09 6.68' 24.06 6.79 25 26 25.11 6.73 25.08 6.84 25.05 6.95 1 25.02 7.06 26 27 26.08 6.99 26.05 7.10 26.02 7.22 25.99 7.33 27 28 27.05 7.25 27.01 7.36 26.98 7.48 26.95 7.60 28 29 28.01 7.51 27.98 7.63 27.95 7.75 27.91 7.87 29 30 28.98 7.76 28.94 7.89 28.91 8.02 28.87 8.14 30 31 29.94 8.02 29.91 8.15 29.87 8.28 29.84 8.41 31 32 30.91 8.28 30.87 8.42 30.84 8.55 30.80 8.69 32 33 31.88 8.54 31.84 8.68 31.80 8.82 31.76 8.96 33 34 32.84 8,80 32.80 8.94 32.76 9.09 32.72 9.23 34 35 33.81 9.06 33.77 9.21 33.73 9.35 33.69 9.50 35 36 34.77 9.32 34.73 9.47 34.69 9.62 34.65 9.77 36 37 35.74 9.58 35.70 9.73 35.65 9.89 35.61 10.04 37 38 36.71 9.84 36.66 10.00 36.62 10.16 36.57 10.31 38 39 37.67 10.09 37.63 10.26 37.58 10.42 37.54 10.59 39 40 38.64 10.35 38.59 10.. 52 38.55 10.69 38.50 10.86 40 41 39.60 10.61 39.56 10.78 39.51 10.96 39.46 11.13 41 42 40.57 10.87 40.52 11.05 40.47 11.22 40.42 11.40 42 43 41.53 11.13 41.49 11.31 41.44 11.49 41.39 11.67 43 44 42.50 11.39 42.45 11.57 42.40 11.76 42.35 11.94 44 45 43.47 11.65 43.42 11.84 43.36 12.03 43.31 12.21 45 46 44.43 11.91 44.38 12.10 44.33 12.29 44.27 12.49 46 47 45.40 12.16 45v35 12.36 45.29 12.56 45.24 12.76 47 48 46.36 12.42 46.31 12.63 46.25 12.83 46.20 13.03 48 49 47.33 12.68 47.27 12.89 47.22 13.09 47.16 13.30 49 50 48.30 12.94 48.24 13.15 48.18 13.36 48.12 13.57 50 Q i Dep. Lat. r| Dep- Lat. Dep. Lat. Dep. Lat. S 1 75 Deg. i 1 74 Deg. .74| Deg. 74iDeg. TK AVERSE TABLE. 3S o 1 "61 15 Deg. I5i Deg. 151 Deg. 151 Deg. D BO P 3 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 49.26 13.20 49.20 13.41 49.15 13.63 49.09 13.84 52 50.23 13.46 50.17 13.68 50.11 13.90 .50.05 14.11 52 53 51.19 13.72 51.13 13.94 51.07 14.16 51.01 14.39 53 54 52.16 13.98 52.10 14.20 .52.04 14.43 51.97 14.66 54 55 53.13 1 14.24 53.06 14.47 53.00 14.70 52.94 14.93 55 56 54.09 14.49 54.03 14.73 53.96 14.97 53.90 15.20 56 57 55.06 14.75 54.99 14.99 54.93 15.23 54.86 15.47 57 58 56.02 15.01 55.96 15.26 55.89 15.. 50 55.82 15.74 58 59 56.99 15.27 56.92 15.52 56.85 15.77 56.78 16.01 59 60 61 57.96 15.53 57.89 15.78 57.82 58.78 16.03 57.75 16.29 60 61 58.92 15.79 58.85 16.04 16.30 58.71 16.56 63 59.89 16.T)5 59.82 16.31 59.75 16.57 59.67 16.83 62 63 60.85 16.31 60.78 16.57 60.71 16.84 60.63 17.10 63 64 61.82 16.56 61.75 16.83 61.67 17.10 61.60 17.37 64 65 62.79 16.82 62.71 17.10 62.64 17.37 62.56 17.64 65 66 63.75 17.08 63.68 17.36 63.60 17.64 63.52 17.92 66 67 64.72 17.34 64.64 17.62 64.56 17.90 64.48 18.19 67 68 65.68 17.60 65.61 17.89 65.53 18.17 65.45 18.46 68 69 66.65 17.86 66.57 18.15 66.49 18.44 66.41 18.73 69 70 71 67.61 18.12 67.54 18.41 67.45 18.71 67.37 19.00 70 71 68.58 18.38 68.50 18.68 68.42 18.97 68.33 19.27 72 69.55 18.63 69.46 18.94 69.38 19.24 69.30 19.54 72 73 70.51 18.89 70.43 19.20 70.35 19.51 70.26 19.82 73 74 71.48 19.15 71.39 19.46 71.31 19.78 71.22 20.09 74 75 72.44 19.41 72.36 19.73 72.27 20.04 72.18 20.36 75 76 73.41 19.67 73.32 19.99 73.24 20.31 73.15 20.63 76 77 74.38 19.93 74.29 20.25 74.20 20.58 74.11 20.90 77 78 75.34 20.19 75.25 20.52 75.16 20.84 75.07 21.17 78 79 76.31 20.45 76.22 20.78 76.13 21.11 76.03 21.44 79 80 81 77.27 20.71 77.18 21.04 77.09 21.38 77.00 21.72 21.99 80 81 78.24 20.96 T8.15 21.31 78.05 21.65 77.96 82 79.21 21.22 79.11 21.57 79.02 21.91 78.92 22.26 82 83 80.17 21.48 80.08 21.83 79.98 22.18 79.88 22.53 83 84 81.14 21.74 81.04 22.09 80.94 22.45 80.85 22.80 84 85 82.10 22.00 82.01 22.36 81.91 22.72 81.81 23.07 85 86 83.07 22.26 82.97 22.62 82.87 22.98 82.77 23.34 86 87 84.04 22.52 83.94 22.88 83.84 23.25 83.73 23.62 87 88 85.00 22.78 84.90 23.15 84.80 23.52 84.70 23.89 88 89 85.97 23.03 85.87 23.41 85.76 23.78 85.66 24.16 89 90 91 86.93 23.29 86.83 23.67 86.73 24.05 86.62 24.43 90 91 87.90 23.55 87.80 23.94 87.69 24.32 87.58 24.70 92 88.87 23.81 88.76 24.20 88.65 24.59 88.55 24.97 92 93 89.83 24.07 89.73 24.46 89.62 24.85 89.51 25.24 93 94 90.80 24.33 90.69 24.72 90.58 25.12 90.47 25.52 94 95 91.76 24.59 91.65 24.99 91.54 25.39 91.43 25.79 95 96 92.73 24.85 92.62 25.25 92.51 25.65 92.40 26.06 96 97 93.69 25.11 93.58 25.51 93.47 25.92 93.36 26.33 97 98 94.66 25.36 94.55 25.78 94.44 26.19 94.32 26.60 98 99 95.63 25.62 95.51 26.04 95.40 26.46 95.28 26.87 99 100 1 96.59 Dep. 25.88 96.48 26.30 96.36 26.72 96.25 27.14 Lat. 100 Lat. Dep. Lat. Dep. Lat. Dep. 75 Deg. T4| Deg. 74| Deg. 74i De;g. 34 TRAVERSE TABLE. 16 Deg. 16i Deg, 161 Deg. 161 Deg. 1 Lat. Dep. Lat. Dep. Lat. Dep. 0.28 Lat. 0.96 Dep. 0.96 0.28 0.96 0.28 0.96 0.29 1 2 1.92 0.55 1.92 0.56 1.92 0.57 1.92 0.58 2 3 2.88 0.83 2.88 0.84 2.88 0.85 2.87 0.86 3 4 3.85 1.10 3.84 1.12 3.84 1.14 3.83 1.15 4 5 4.81 1.38 4.80 1.40 4.79 1.42 4.79 l.M 5 6 5.77 1.65 5.76 1.68 5.75 1,70 5.75 1.73 6 7 6.73 1.93 6.72 1.96 6.71 1.99 6.70 2.02 7 8 7.69 2.21 7.68 2.24 7.67 2.27 7.66 2.31 8 9 8.65 2.48 8.64 2.52 8.63 2.56 8.62 2.59 9 10 n 9.61 10.57 2.76 9.60 2.80 9.59 2.84 9.58 2.88 10 11 3.03 10.56 3.08 10.55 3.12 10.53 3.17 12 11.54 3.31 11.52 3.36 11.51 3.41 11.49 3.46 12 13 12.50 3.58 12.48 3.64 12.46 3.69 12.45 3.75 13 14 13.46 3.86 13.44 3.92 13.42 3.98 13.41 4.03 i 14 I 15 14.42 4.13 14.40 4.20 14.38 4.26 14.36 4.32 15 16 15.38 4.41 15.36 4.48 15.34 4.54 15.32 4.61 16 17 16.34 4.69 16.32 4.76 16.30 4.83 16.28 4.90 17 18 17.30 4.96 17.28 5.04 17.26 5.11 17.24 5.19 18 19 18.26 5.24 18.24 5.32 18.22 5.40 18.19 5.48 19 20 19.23 5.51 19.20 5.60 19.18 5.68 19.15 5.76 20 21 20.19 5.79 20.16 5.88 20.14 5.96 20.21 6.05 21 22 21.15 6.06 21.12 6.16 21.09 6.25 21,07 6.34 1 22 1 23 22.11 6.34 22.08 6.44 22.05 6.53 23.02 6.63 23 24 23.07 6.62 23.04 6.72 23.01 6.82 22.98 6.92 24 2f) 24.03 6.89 24.00 7.00 23.97 7.10 23.94 7.20 25 26 24.99 7.17 24.96 7.28 24.93 7.38 24.90 7.49 26 27 25.95 7.44 25.92 7.56 25.89 7.67 25.85 7.78 27 28 26.92 7.72 26.88 7.84 26.85 7.95 26.81 8.07 28 29 27.88 7.99 27.84 8.11 37.81 8.24 27.77 8.36 29 30 31 28.84 29.80 8.27 28.80 8.39 28.76 8.52 28.73 8.65 30 8.54 29.76 8.67 29.72 8.80 29.68 8.93 31 32 30.76 8.82 30.72 8.95 30.68 9.09 30.64 9.22 32 33 31.72 9.10 31.68 9.23 31.64 9.3/ 31.60 9.51 33 34 32.68 9.37 32.64 9.51 32.60 9.66 32.56 9.80 34 35 33.64 9.65 33.60 9.79 33.56 9.94 33.51 10.09 35 36 34.61 9.92 34.56 10.07 34.52 1C.22 34.47 10.38 36 37 35.57 10.20 35.52 10.35 35.48 10.51 35.43 10.66 37 3S 36.53 10.47 36.48 10.63 36.44 10.79 36.39 10.95 38 39 37.49 10.75 37.44 10.91 37.39 11.08 37.35 n.24 39 40 41 38.45 11.03 38.40 11.19 .38.35 11.36 38.30 11.53 11.82 40 41 39.41 11.30 39.36 11.47 39.31 11.64 39.26 42 40.37 11.58 40.32 11.75 40.27 11.93 40.22 12.10 42 43 41.33 11.85 41.28 12.03 41.23 12.21 41.18 12.39 43 44 42.30 12.13 42.24 12.31 42.19 12.50 42.13 12.68 44 45 43.26 12.40 43.20 12.59 43.15 12.78 43.09 12.97 45 46 44.22 12.68 44.16 12.87 44.11 13.06 44.05 13,26 46 47 45.18 12.95 45.12 13.15 45.06 13.35 45.01 13.55 47 48 46.14 13.23 46.08 13.43 46.02 13.63 45.96 13.83 48 49 47.10 13.51 47.04 13.71 46.98 13.92 46.92 14.12 49 50 1 .a 48.06 Dep. 13.78 48.00 13.99 47.94 14.20 47.88 14.41 Lat. 50 1 (5 Lat. Dep. Lat. Dep. Lat. Dep. 74 Deg. 731 Deg. 73i Deg. T3i Deg. TRAVEESE TABLE. 35 p 51 16 Deg. 16i Deg. 16^ Deg. 161 Deg. 1 ? "51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 49.02 14.06 48.96 14.27 48.90 14.48 48.84 14.70 o2 49.99 14.33 49.92 14.55 49.86 14.77 49.79 14.99 52 53 50.95 14.61 50.88 14.83 50.82 15.06 50.75 15.27 63 54 51.91 14.88 51.84 15.11 51.78 15.34 61.71 15.56 54 55 52.87 15.16 52.80 15.39 52.74 15.62 62.67 16.85 55 58 .'13.83 15.44 53.76 15.67 63.69 15.90 63.62 16.14 56 57 54.79 15.71 54.72 15.95 54.65 16.19 54.68 16.43 57 58 55.75 15.99 55.68 16.23 55.61 16.47 56.64 16.72 58 59 56.71 16.26 56.64 16.51 56.57 16.76 66.50 17.00 69 60 61 57.68 16.54 57.60 16.79 57.53 17.04 57.46 17.29 60 61 58.64 16.81 58.56 17.07 58.49 17.32 58.41 17.58 62 59.60 17.09 59.52 17.35 69.45 17.61 59.37 17.87 62 63 60.56 17.37 60.48 17.63 60.41 17.89 60.33 18.16 63 64 61.52 17.64 61.44 17.91 61.36 18.18 61.28 18.44 64 65 62.48 17.92 62.40 18.19 62.32 18.46 62.24 18.73 65 66 63.44 18.19 63.36 18.47 63.28 18.74 63.20 19.02 66 67 64.40 18.47 64.32 18.75 64.24 19.03 64.16 19.31 67 68 65.. 37 18.74 65.28 19.03 66.20 19.31 65.11 19.60 68 69 66.33 19.02 66.24 19.31 66.16 19.60 66.07 19.89 69 70 71 67.29 19.29 67.20 19.59 67.12 19.88 67.03 20.17 70 71 68.25 19.57 68.16 19.87 68.08 20.17 67.99 20.46 72 69.21 19.85 69.12 20.15 69.03 20.45 68.95 20.76 72 73 70.17 20.12 70.08 20.43 69.99 20.73 69.90 21.04 73 74 71.13 20.40 71.04 20.71 70.95 21.02 70.86 21.33 74 75 72.09 20.67 72.00 20.99 71.91 21.30 71.82 21.61 76 76 73.06 20.95 72.96 21.27 72.87 21.69 72.78 21.90 76 77 74.02 21.22 73.92 21.55 73.83 21.87 73.73 22.19 77 78 74.98 21.. 50 74.88 21.83 74.79 22.15 74.69 22.48 78 79 75.94 21.78 75.84 22.11 75.75 22.44 75.65 22.77 79 80 81 76.90 22.05 76.80 22.39 76.71 22.72 76.61 23.06 80 81 77.86 22.33 77.76 22.67 77.66 23.01 77.56 23.34 82 78.82 22.60 78.72 22.95 78.62 23.29 78.62 23.63 82 83 79.78 22.88 79.68 23.23 79.58 23.57 79.48 23.92 83 84 80.75 23.15 80.64 23.51 80.54 23.86 80.44 24.21 84 85 81.71 23.43 81.60 23.79 81.50 24.14 81.39 24.60 85 86 82.67 23.70 82.56 24.07 82.46 24.43 82.35 24.78 86 87 83.63 23.98 83.52 24.35 83.42 24.71 83.31 25.07 87 88 84.59 24.26 84.48 24.62 84., 38 24.99 84.27 25.36 88 89 85.55 24.53 85.44 24.90 85.33 25.28 86.22 26.65 89 90 91 86.51 24.81 86.40 25.18 86.29 26.66 86.18 25.94 90 91 87.47 25.08 87.36 25.46 87.26 26.85 87.14 26.23 92 88.44 25.36 88.32 25.74 88.21 26.13 88.10 26.51 92 93 89.40 25.63 89.28 26.02 89.17 26.41 89.06 26.80 93 94 90.36 25.91 90.24 26.30 90.13 26.70 90.01 27.09 94 95 91.32 26.19 91.20 26.58 91.09 26.98 90.97 27.38 95 96 92.28 26.46 92.16 26.86 92.05 27.27 91.93 27.67 96 97 93.24 26.74 93.12 27.14 93.01 27.55 92.88 27.95 97 98 94.20 27.01 94.08 27.42 93.96 27.83 93.84 28.24 98 99 95.16 27.29 95.04 27.70 94.92 28.12 94.80 28.53 99 100 £ 96.13 27.56 96.00 27.98 95.88 28.40 95.76 28.82 100 .2 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 74 Deg. 731 Deg. 73^ Deg. 73i Deg. N 36 TRAVERSE TABLE. a 17 Deg-. I7i Deg. iH] Deg. 171 Deg. s E o a> Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. ~1 0.96 0.29 0.95 0.30 0.95 0.30 0.95 0.30 2 1.91 0.58 1.91 0.59 1.91 0.60 1.90 0.61 2 3 ! 2.87 0.88 2.87 0.89 2.86 0.90 2.86 0.91 3 4i 3.83 1.17 3.82 1.19 3.81 1.20 3.81 1.22 4 5 4.78 1.46 4.78 1.48 4.77 1.50 4.76 1,52 5 6 5.74 1.75 5.73 1.78 6.72 1.80 5.71 1.83 6 7 6.69 2.05 6.69 2.08 6.68 2.10 6.67 2.13 7, 8 7.66 2.34 7.64 2.37 7.63 2.41 7.62 2.44 8 9 8.61 2.63 8.60 2.67 8.68 2.71 8.57 2.74 9 10 11 9.56 2.92 9.55 2.97 9.54 3.01 9.52 3.05 10 11 10.62 3.22 10.51 3.26 10.49 3.31 10.48 3.35 12 11.48 3.51 11.46 3.. 56 11.44 3.61 11.43 3,66 12 13 12.43 3.80 12.42 3.85 12.40 3.91 12.38 3.96 13 14 13.39 4,09 13.37 4.15 13.36 4.21 13.33 4.27 14 15 14.34 4.39 14.33 4.45 14.31 4.51 14.29 4.57 15 16 15.30 4.68 15.28 4.74 15.26 4.81 15.24 4.88 16 17 16.26 4.97 16.24 5.04 16.21 5.11 16.19 5.18 17 18 17.21 5.26 17.19 5.34 17.17 5.41 17.14 6.49 18 19 18.17 5.56 18.15 5.63 18.12 5.71 18.10 5.79 19 20 21 19.13 5.85 19.10 20.06 6.93 19.07 6.01 19.05 6.10 20 21 20.08 6.14 6.23 20.03 6.31 20.00 6.40 22 21.04 6.43 21.01 6.52 20.98 6.62 20.95 6.71 22 23 21.99 6.72 21.97 6.82 21.94 6.92 21.91 7.01 23 24 22.95 7.02 22.92 7.12 22.89 7.22 22.86 7.32 24 2o 23.91 7.31 23.88 7.41 j 23.84 7.52 23.81 7.62 25 26 24.86 7.60 24.83 7.71 24.80 7.82 24.76 7.93 26 27 25.82 7.89 25.79 8.01 26.75 8.12 25.71 8.23 27 28 26.78 8.19 26.74 8.30 26.70 8.42 26.67 8.54 28 29 27.73 8.48 27.70 8.60 27.66 8.72 27.62 8.84 29 30 31 28.69 i 8.77 28.66 8.90 28.61 9.02 28.57 9.15 30 31 29.65 i 9.06 29.61 9.19 29.57 9.32 29.52 9.46 32 30.60! 9.36 30.56 9.49 30.52 9.62 30.48 9.76 32 33 31.561 9.65 31.62 9.79 31.47 9.92 31.43 10.06 33 34 32.51! 9.94 32.47 10.08 32.43 10.22 32.38 10.37 34 35 33.47! 10.23 33.43 10.38 33.38 10.. 52 33.33 10.67 35 36 34.43 10.53 34.38 10.68 34.33 10.83 34.29 10.98 36 37 36.38: 10.82 35.34 10.97 36.29 11.13 35 24 11.28 37 38 36.341 11.11 36.29 11.27 36.24 11.43 36.19 11. .58 38 39 37.30 11.40 37.25 11. .57 37.19 11.73 37.14 11.89 39 40 41 38.25 11.69 38.20 11.86 38.15 12.03 38.10 12.19 40 41 39.21 11.99 39.16 12.16 39.10 12.33 39.05 12.50 42 40.16 i 12.28 40.11 12.45 40.06 12.63 40.00 12.80 42 43 41.12: 12.57 141.07 12.75 41.01 12.93 40.96 13.11 43 44 42.08 12.86 42.02 13.05 41.96 13.23 41.91 13.41 44 45 43.03 13.16 42.98 13.34 42.92 13.53 42.86 13.72 45 46 43.99 13.45 ! 43.93 13.64 43.87 13.83 43.81 14.02 46 47 44.95 13.74 44.89 13.94 44.82 14.13 44.76 14.33 47 48 45.90 14.03 45.84 14.23 45.78 14.43 45.71 14.63 48 49 46.86 14.33 46.80 14.. 53 46.73 14.73 46.67 14.94 49 JO i w 47.82 14.62 1 47.75 14.83 47.69 15.04 47,62 15.24 60 o - 1 s Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 73 Deg. 721 Deg. - Deg. 72i Deg. TRAVERSE TABLE. 31 5 5 3 9 51 17 Deg. 17i Deg. m l^eg. 171 Deg. 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 48.77 14.91 48.71 15.12 48.64 15,34 48.57 15.65 61 52 49.73 15.20 49.66 15.42 49.59 15.64 49.52 15.85 52 53 50.68 15.50 50.62 15.72 50.65 15.94 50.48 16.16 53 54 51.64 15.79 51.57 1 16.01 51,50 16.24 51.43 16.46 54 55 52.60 16.08 52.53 1 16.31 52.45 16.54 52.38 16.77 55 56 53.55 16.37 53.48 16.61 53.41 16.84 53.33 17.07 56 57 54.51 16.67 54.44 16.90 54.. 36 17.14 54.29 17.38 57 58 55.47 16.96 55.39 17.20 55.32 17.44 .55.24 17.68 58 59 56.42 17.25 56,35 17.60 56.27 17.74 56.10 17.99 69 60 61 57.38 17.54 17.83 57.30 17.79 57.22 18.04 57.14 18.29 60 58.33 58.26 18.09 58.18 18.34 58.10 18.60 61 62 59.29 18.13 59.21 18.39 59.13 18.64 .59.05 18.90 62 63 60.25 18.42 60.17 18.68 60.08 18.94 60.00 19.21 63 64 61.20 18.71 61.12 18.98 61.04 19.25 60,95 19.51 64 65 62.16 19.00 62.08 19.28 61.99 19.55 61.91 19.82 65 66 63.12 19.30 63.03 19.57 62.95 19.85 62,86 20.12 66 67 64.07 19.59 63.99 19.87 63.90 20.15 63.81 20.43 67 68 65.03 19.88 64.94 20.16 64.85 20.45 64,76 20.73 68 G9 65.99 20.17 65.90 20.46 65.81 20.75 65.72 21.04 69 70 71 66.94 20.47 66.85 20.76 66.76 21.05 66.67 21.34 70 71 67.90 20.76 67.81 21.05 67.71 21.35 67.62 21.65 72 68.85 21.05 68.76 21.35 68.67 21.65 68.57 21.95 72 73 69.81 21.34 69.72 21.65 69.62 21.95 69.52 22.26 73 74 70.77 21.64 70.67 21.94 70.58 22.25 70.48 22.56 74 75 71.72 21.93 71.63 22.24 71.53 22.55 71.43 22.86 75 76 72.68 22.22 72.58 22.54 72.48 22.85 72,38 23.17 76 77 73.64 22.51 73.54 22.83 73.44 23.15 73.33 23.47 77 78 74.59 22.80 74.49 23.13 74.39 23.46 74,29 23.78 78 79 75.55 23.10 75.45 23.43 i 75.34 23.76 75.24 24.08 79 80 81 76.50 23.39 76.40 23.72 1 76.. 30 24.06 76.19 24.39 80 77.46 23.68 77.36 24.02 77.25 24.36 77.14 24.69 81 82 78.42 23.97 78.31 24.32 1 78.20 24.66 78,10 25.00 82 83 79.37 24.27 79.27 24.61 ; 79.16 25.96 79,05 25.30 83 84 80.33 24.56 80.22 24.91 ■ 80.11 25.26 80,00 25,61 84 85 81.29 24.85 81.18 25.21 i 81.07 25.56 80,95 25,91 85 86 82.24 25.14 82.13 25.50 82.02 25.86 81.91 26,22 86 87 83.20 25.44 83.09 25.80 82.97 26.16 82.86 26,52 87 88 84.15 26.73 84.04 26.10 83.93 26.46 83,81 26,83 88 89 85.11 26.02 85.00 26.39 84.88 26.76 84.76 27.13 89 90 91 86.07 26.31 85.95 26.69' 85.83 27.06 85.72 27.44 90 87.02 26.61 86.91 26.99 86.79 27.36 86.67 27.74 91 92 87.98 26.90 87.86 27.28 i 87.74 27.66 87.62 28.05 98 93 88.94 27.19 88.82 27.58 88.70 27.97 88.57. 28.35 93 94 89.89 27.48 89.77 27.87 89.65 28.27 89.53 28.66 94 95 90.85 27,78 90.73 28.17 90.60 28.57 90.48 28.96 95 96 91.81 28.07 91.68 28.47 91. .56 28.87 91.43 29.27 96 97 92.76 28.. 36 92.64 28.76 92.51 29.17 92.38 29.57 97 98 93.72 28.65 93.59 29.06 93.46 29.47 93.33 29.88 98 99 94.67 28.94 94.55 29.36 94,42 29.77 94.29 30.18 99 100 aJ o c s 5 95.63 29.24 .95.50 29.65 95.37 .30.07 95.24 30.49 100 Dep. Lat. Dep. Lat. ^ Dep. Lat. Dep. Lat.' 1 5 73 Deg. 721 Deg. 72i Deg. 72i Deg. 38 TRAVERSE TABLE. D 1 18 Deg. 18i Deg. 18^ Deg. 18| Deg. ? 1 Lai. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.95 0.31 0.95 0.31 0.95 0.32 0.95 0.32 2 1.90 0.62 1.90 0,63 1.90 0.63 1.89 0.64 2 3 2.85 0.93 2.85 0.941 2.84 0.95 2.84 0.96 3 4 3.80 1.24 3.80 1.25 3.79 1.27 3.79 1.29 4 5 4.76 1.55 4.75 1.57 4.74 1.59 4.73 1.61 5 6 5.71 1.85 5.70 1.88 5.69 1.90 5.68 1.93 6 7 6.66 2.16 6.65 2.19 6.64 2.22 6.63 2.25 7 8 7.61 2.47 7.60 2 = 51 7.59 2.54 7.58 2.57 8 9 8.56 2.78 8.55 2.82 8.53 2.86 8.52 2.89 9 10 11 9.51 3.09 9.50 3.13 9.48 3.17 9.47 3.21 10 10.46 3.40 10.45 3.44 10.43 3.49 10.42 3.54 11 12 11.41 3.71 11.40 3.76 11.38 3.81 11.36 3.86 12 13 12.36 4.02 12.35 4.07 12.33 4.12 12.31 4.18 13 14 13.31 4.33 13.30 4.38 13.28 4.44 13.26 4.50 14 15 14.27 4.64 14.25 4.70 14.22 4.76 14.20 4.82 15 16 15.22 4.94 15.20 5.01 15.17 5.08 15.15 5.14 16 17 16.17 5.25 16.14 5.32 16.12 5.39 16.10 5.46 17 18 17.12 5.56 17.09 5.64 17.07 5.71 17.04 5.79 18 19 18.07 5.87 18.04 5.95 18.02 6.03 17.99 6.11 19 20 21 19.02 6.18 18.99 6.26 1 18.97 6.35 18.94 6.43 20 19.97 6.49 19.94 6.58 19.91 6.66 19.89 6.75 21 22 20.92 6.80 20.89 6.89 20.86 6.98 20.83 7.07 22 23 21.87 7.11 21.84 7.20 21.81 7.30 21.78 7.39 23 24 22.83 7.42 22.79 7,52 22.76 7.62 22.73 7.71 24 25 23.78 7.73 23.74 7.83 23.71 7.93 23.67 8.04 25 26 24.73 8.03 24.69 8.14 24.66 8.25 24.62 8.36 26 27 25.68 8.34 25.64 8.46 25.60 8.57 25.57 8.68 27 28 26.63 8.65 26.59 8.77 26.55 8.88 26.51 9.00 28 29 27.58 8.96 27.54 9.08 27.50 9.20 27.46 9.32 29 30 28.53 9.27 28.49 9.39 28.45 9.52 28.41 9.64 30 31 29.48 9.58 29.44 9.71 29.40 9.84 29.35 9.96 31 32 30.43 9.89 30.39 10.02 30.35 10.15 30.30 10.29 32 33 31.38 10.20 31.34 10.33 31.29 10.47 31.25 10.61 33 34 32.34 10.51 32.29 10.65 32.24 10.79 32.20 10.93 34 35 33.29 10.82 33.24 10.96 33.19 11.11 33.14 11.25 35 36 34.24 11.12 34.19 11.27 34.14 11.42 34.09 11.57 36 37 35.19 11.43 35.14 11.59 35.09 11.74 35.04 11.89 37 38 36.14 11,74 36.09 11.90 36.04 12.06 35.98 12.21 38 39 37.09 12.05 37.04 12.21 36.98 12.37 36.93 12.54 39 40 38.04 12.36 37.99 12.53 37.93 12.69 37.88 12.86 13.18 40 41 41 38.99 12.67 38.94 12.84 38.88 13.01 38.82 42 39.94 12.98 39.89 13.15 39.83 13.33 39.77 13.50 43 43 40.90 13.29 40.84 13.47 40.78 13.64 40.72 13.82 43 44 41.85 13.60 41.79 13.78 41.73 13.96 41.66 14.14 44 45 42.80 13.91 42.74 14.09 42.67 14.28 42.61 14.46 45 46 43.75 14.21 43.69 14.41 43.62 14.60 43.56 14.79 46 47 44.70 14.52 44.64 14.72 44.57 14.91 44.51 15.11 47 48 45.65 14.83 45.59 15.03 45.52 15.23 45.45 15.43 48 49 46.60 15.14 46.54 15.35 46.47 15.55 46.40 r5.75 49 50 47.55 15.45 47.48 15.66 47.42 15.87 47.35 16.07 60 6 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. l_ 72 Deg. 7l| Deg. 7H Deg. 7U Deg. TE AVERSE TABLE. 39 s 18 Deg. 184 Deg. 18i Deg. 18| Deg. 1 ti 9 51 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 48.50 15.76 48.43 15.97 48.36 16.18 48.29 16.39 52 49.45 16.07 1 49.38 16.28 49.31 16.50 49.24 16.71 52 53 50.41 16.38 1 50.33 16.60 50.26 16.82 50.19 17.04 53 54 51.36 16.69 1 51.28 16.91 51.21 17.13 51.13 17.36 54 55 52.31 17.00 52.23 17.22 52.16 17.45 52.08 17.68 55 56 53.26 17.30 53.18 17.54 53.11 17.77 53.03 18.00 56 57 54.21 17.61 54.13 17.85 54.05 18.09 53.98 18.32 57 58 55.16 17.92 55.08 18.16 55.00 18.40 54.92 18.64 58 59 56.11 18,23 56.03 18.48 55.95 1 18.72 55.87 18.96 59 60 61 57.06 58.01 18.54 18 85 56.98 18.79 56.90 19.04 56.82 19.29 60 61 57.93 19.10 57.85 19.36 57.76 19.61 62 58.97 19.16 .58.88 19.42 58.80 19.67 58.71 19.93 62 63 59.92 19.47 59.83 19.73 59.74 19.99 59.66 20.25 63 64 60.87 19.78 60.78 20.04 60.69 20.31 60.60 20.57 64 65 61.82 20,09 61.73 20.36 61.64 20.62 61.55 20.89 65 66 62.77 20.40 62.68 20.67 62.59 20.94 62.50 21.22 66 67 63.72 20.70 63.63 20.98 63.54 21.26 63.44 21.54 67 68 64.67 21.01 64.58 21.30 64.49 21.58 64.39 21.86 68 69 65.62 21.32 65.53 21.61 65.43 21.89 65.34 22.18 69 70 71 66.57 21.63 21.94 66.48 67.43 21.92 66.38 67.33 22.21 66.29 22.50 22.82 70 71 67.53 22.23 22.53 67.23 72 68.48 22.25 68.38 22.55 68.28 22.85 68.18 23.14 72 73 69.43 22.56 69.33 22.86 69.23 23.16 69.13 23.47 73 74 70.38 22.87 70.28 23.17 70.18 23.48 70.07 23.79 74 75 71.33 23.18 71.23 23.49 71.12 23.80 71.02 24.11 75 76 72.28 23.49 72.18 23.80 72.07 24.12 71.97 24.43 76 77 73.23 23.79 73.13 24.11 73.02 24.43 72.91 24.75 77 78 74.18 24.10 74.08 24.43 73.97 24.75 73.86 25.07 78 79 75.13 24.41 75.03 24.74 74.92 25.07 74.81 25.39 7S 80 81 76.08 77.04 24.72 25.03 75.98 25.05 75.87 25.38 75.75 25.72 26.04 80 81 76.93 25.37 76.81 25.70 76.70 82 77.99 25.34 77.88 25.68 77.76 26.02 77.65 26.36 1 82 1 83 78.94 25.65 78.83 25.99 78.71 26.34 78.60 26.68 ! S?A 84 79.89 25.96 79.77 26.31 79.66 26.65 79.54 27.00 84 85 80.84 26.27 80.72 26.62 80.61 26.97 80.49 27.32 85 86 81.79 26.58 81.67 26.93 81.56 27.29 81.44 27.64 86 87 82.74 26.88 82.62 27.25 82.50 27.61 82.38 27.97 87 88 83.69 27.19 83.57 27.56 83.45 27.92 83.33 28.29 88 89 84.64 27.50 84.52 27.87 84.40 28.24 84.28 28.61 85 90 91 85.60 27.81 85.47 28.18 85.35 28.56 28.87 85.22 28.93 90 86.55 28.12 86.42 28.50 86.30 86.17 29.25 91 92 87.50 28.43 87.37 28.81 87.25 29.19 87.12 29.57 92 93 88.45 28.74 88.32 89.27 29.12 88.19 29.51 88.06 29.89 93 94 89.40 29.05 29.44 89.14 29.83 89.01 30.22 94 95 90.35 29.. 36 90.22 29.75 90.09 30.14 89.96 30.54 95 96 91.30 29.67 91.17 30.06 91.04 30.46 90.91 30.86 96 97 92.25 29.97 92.12 30.38 91.99 30.78 91.85 31.18 97 98 93.20 30.28 93.07130.69 92.94 31.10 92.80 31.. 50 98 99 94.15 30.. 59 94.02 31.00 93.88 31.41 93.75 31.82 99 100 1 95.11 30.90 94.97 31.32 94.83 31.73 94.69 32.14 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 72 Deg. 711 Deg. 71|Deg. m Deg. 40 TRAVLRaE TAELL. 19 Deg. i! 19i Deg. 1! ij mDeg. ! 191 Deg. i •' 2 1 Lat. Dep. J! Lat..^ Dep. 1 L... Dep. 0.33 II Lat. 1 Dep. 1 0.95 0.33 ii 0.94 0.33 ' 0.94 '! 0.94; 0.34 2 1.89 0.65 '1 1.89 0.66 ; 1.89 0.67 'j 1.88; 0.68 2 3 2.84 0.98 'i 2.83 0.99 ; 2.83 1.00 : 2.82' 1.01 3 4 3.78 1.30 :i 3.78 1.32 !; 3.77 1.34 ii 3.76 1 1.35 4 5 4.73 1.63 !' 4.72 1.65 \\ 4.71 1.67 :; 4.71 1.69 5 6 5.67 1.95 : 5.66 1.98 II 5.66 2.31 ! 6.60 2.00 :l 5.65 2.03 6 7 6.62 2.28 : 6.61 2.34 j 6.59 2.37 7 8 7.56 2.60 7.55 2.64; 7.54 2.67 7.53 2.70 8 9 8.51 2.93 8. .50 2.97! 8.48 3.00 1 8.47 3.04 9 10 9.46 I 3.26 9.44 3.30 j! 9.43 3.34 ; 9.411 3.38 ]0 11 11 10.40 3.58 10.38 3.63 ! 10.37 3.67 10.35: 3.72 12 11.35 3.91 11.33i 3.96 ;! 11.31 4.01 11.29; 4.06 12 13 12.29 4.23 12.27 i 4.29 I! 12.25 4.34 i 12.24; 4.39 13 14 13.24 4.56 13.22! 4.62 jl 13.20 4.67 ! 13.18 4.73 14 15 14.18 4.88 14.l6i 4.95 14.14 5.01 • 14.12 5.07 15 16 15.13 5.21 15.11 5.28 15.08 5.34 15.06 i 5.41 16 17 16.07 5.53 16.05 5.60 i; 16.02 5.67 : 16.00 1 5.74 17 18 17.02 1 5.86 16.99 5.93 1116.97 6.01 16.94! 6.08 18 19 117.96 6.19 17.94 i 6.26 ;i 17.91 i 6.34 17.88 ! 6.42 19 20 1 18.91 6.51 18.88 ; 6.59 :; 18.85 1 6.68 19.83 6.92,1 19.80 i 7.01 18.82 1 6.76 19.76 1 7.10 20 21 21 19.86 6.84 22 20.80 7.16 20.77 7.25 20.74 7.34 20.71 7.43 22 23 21.75 7.49 21.71 7.58:121.68 7.68 21.65 7.77 23 24 22.69 7.81 22.66 7.91 (22.62 8.01 22.59 8.11 24 25 23.64 8.14 23.60 8.24 8.57 23.57 8.35 23.53 8.45 25 26 24.58 8.46 24.55 24.51 8.68 i 24.47 1 8.79 26 27 25.53 8.79 25.49 8.90 25.45 9.01 - 25.41 i 9.12 27 28 26.47 9.12 26.43 9.23! 26.39 9.35' 26 . 35 9.46 28 29 27.42 9.44 27.38 9.66 27.34 9.68- 27.29 9.80 29 30 28.37 9.77 2S.32 9.89 : 28.28 10.01 : 10.35 28.24 10.14 30 31 29.31 10.09 1 29.27! 10.22 < 29 . 22 29.18 10.48 3i 32 30.26 10.42 i 30.21 1 10.55 1 30.16 10.681 30.12 10.81 32 33 31.20 10.74; 31.15! 10.88 ; 31.11 11.02 31.06 11.15 33 34 32.15 1 11.07 32.10 11.21; 11.54! 32.05 11.35 32.00 11.49 34 .35 133.09 11.39 i 33.04 32.99 11.68 32.94 11.83 35 36 i 34.04' 11.72 ! 33.99 11.87! 33.94 12.02' 33.88 12.17 36 37 134.98 ' 12.05 ' 34.93: 12.20 1 34.88 12.35 34.82 12.50 37 38 j 35.93 12.37 1 35.88 i 12.53 35.82 ' 12.68; 35.76 12.84 38 39 136.88 : 12.70 36.82 12.86 1 36.76 j 13.02 36.71 1 13.18 39 40 37.82 ! 13.02 41 i 38.77 i 13.35 37.76 13.19 j 38.71 13.52 ; 37.71 13.35! 37.65 1 13.52 40 38.65 13.69 1 38.59 i 13.85 41 42 39.71 i 13.67 \ 39.65 13.85 39.59 14.02' 39.53 1 14.19 42 43 40.66 ; 14.00 \ 40.60' 14.18 ; 40.53 14.35; 40.47 114.53 43 44! 41.60 14.32 1 41.54; 14.51 1 41.48 14.69' 41.41 14.87 44 45 42.55 14.65 42.48: 14.84 1 42.42 15.02: 42.35 15.21 45 46 143.49 14.98 43.43' 15.17 1, 43.36 15.36! 43.29 15.54 46 47 144.44 15.30 1 44.37 i 15.50 ji 44.30 15.69 1 44.24 1 15.8S1 47 48 145.38 15.63 45.32. 15.83 j 45.25 16.02 1 45.18 16.22 43 49 1 46.33 15.95 46.26! 16.15 i 46.19 16.36 i 46.12 16.56 49 50 ; 47.28; 16.28 ; 47.20 i 16.48 j 47.13 16.69 j Lat. ! 47.06 Dep. 16.90 50 1 Dep. Lat. ; Dep. 1 Lat. Dep. Lat. g 5 s 71 Deg. 701 Deg. TQiDeg. 1 70^ Deg. TB AVERSE TABLE. 41 i" - 51 19 Deg. i 19^ Deg. 19| Dog-. 191 Deg. O 1 o ? "51 Lat. 1 Dep. Lat. Dep. 1 Lat. Dep. Lat. Dep. 48.22 i 16.60 ','48. 15 16.81 1 48.07 17.02 48.00 17.23 52 49.17; 16.93 1149.09 17.14 49.02 17.36 48.94 17.57 52 53 50.11 1 17.26!! 50.04 17.47 |i 49.96 17.39 49.88 17.91 53 54 51.06 i 17.58 50.98 52.00 1 17.91 51.92 17.80 jl 50.90 18.03 .50.82 18.25 54 55 18.13 ij 18.46! 51.85 18.36 51.76 18.59 55 56 52.95 1 18.23 1 52.87 .52.79 18.69 52.71 18.92 1 66 57 53.89 i 18.56 ; 53.81 18.79 1 53.73 19.03 53.65 19.26 1 57 58 54.84 i 18.88! 54.76 19.12 i 54.67 19.33 54.59 19.60 58 59 55.79! 19.21 ! 55.70! 19.45! 55.62 19.69 55.53 19.94 59 60 61 56.73 1 19.53 i 56.65 19.78 1 56.56 20.03 20,36 56.47 20.27 60 "61 57.68 i 19.86! 57.59 20.11 1 57.50 57.41 20.61 62 58.62 120.19 .58.53 20.44! 58.44 20.70 58.35 20.95 62 63 59.57 20.51 59.48 20.77 59.39 21.03 1 59.29 21.29 63 64 60.51 20.84 60.42 21.10 60.33 21.36 60.24 21.63 64 65 61.46 21.16 61.37 21.43 61.27 2i.70 61.18 21.96 65 66 62.40 121.49 62.31 21.76 62.21 22.03 62.12 22.30 66 67 63.35 ; 21.81 63.25 22.09 63.16 22.37 63.05 22.64 67 68 64.30 1 22.14 64.20 22.42 64.10 22.70 64.00 22.98 68 69 65.24 22.40 65.14 22.75; 85.04 23.03 64.94 23.32 69 70 71 66. L9 22.79 66.09 23.08 i65.9S 23.37 65 . 88 23.65 70 71 67.13 23.12 67.03 23.41 66.93 23.70 66.82 23.99 72 68.08 23.44 67.97 23.74 67 . .'^^ ; 24.LI3 67.76 24.33 72 73 69.02 23.77 68.92 24.07 68. 8 i 24.37 68.71 24.67 73 74 69.97 24.09 69.86 24.40 69.76 24.70 69.65 25.01 74 75 70.91 24.42 70.81 24.73 70.70 25.04 70.59 25.34 75 76 71.86 24.74 71.75 25.06 71.04 25.37 71.53 25.68 78 77 72.80 25.07' 72.69 25.39 72 . 5S 25 . 70 ' 72.47 26.02 77 78 73.75 25.39 73.64 25.72 ii 73.53 26.04 ! 73.41 26.36 78 79 74.70 25.72 74.58 26.05 |74,4'>' 26 = 37 i 74.35 26.70 79 80 81 75.64 26.05 75..53I 26.38 75.41 26. ?0 i 75.29 27.03 80 8i 76.59 I 26.37 76.47 26.70 76.35 27.04 1 76.24 27.37 82 77.53 26.70 77.42 27.03 77 . 30 27.37 1 77.18 27.71 82 83 78.48 27.02 78.36 27.36 78.24 2?. 71 ! 78.12 28.05 83 84 79.42 27.35 79.30 1 27.69 79. i 8 2?, 04 ; 79.06 28.39 84 85 80.37 27.67 80.25 28.02 8C . ! 2 2S.37 ! 80.00 28 . 72 85 86 81.31 28.00 81. Id 128.35 8i.07 28.71 180.94 29.06 86 87 82.26 28.32 82.14 128.68 82. 'Jl 29.04 ;i 81.88 29.40 87 88 83.21 28.65 83.08 29.01 92 . 95 29..37 11 82.82 29.74 88 89 84.15 28.98 84.02 29.34 83.90 29.71 1183.76 30.07 89 90 '91 85.10 29.30 84.97 29.67 84 - S4 30.04 Ij 84.71 1 85.65 30.41 90 91 86.04 29 . 63 85.91 1 30.00 1 85 . 78 30 . 38 30.75 92 86.99 29.95 86.86 30.33 186.72 30.71 86.59 31.09 92 93 87.93 30.28 87.80 30.66 187.67 3i.04 187.. 53 88.47 189.41 31.43 93 94 88.88 30.60 88.74 30.99 88.81 31.38 31.76 94 95 89.82 30.93 89.69 31.32 89.. 55 31.71 32.10 95 96 90.77 31.25 90.63 31.65 90.49 32.05 90.35 32.44 9^; 97 91.72 31.58 91.58 31.98 91.44 32.38 1 91.29 32 . 78 9? 98 92.66 31.91 92.52 32.31 92 . 38 32.71 92.24 33.12 98 99 93.61 32.23 93.46 32.64 93 32 33.05 ! 93.18 33.45 99 100 i 94.55 32.56 94.41 32.97 94 26 33.38 1 94.12 33.79 Lat. 100 a .2 Dep. Lat. Dep. Lat. Dsp. Lat. Dep. 71 Deg. 70f Deg. TOi Deg. 70; i>eg 42 TSAVEESE TABLE. g ~1 20 Deg. J! 20+ Deg. 20^ Deg. i; 201 Dog. C i i Lat. 1 Dep. 1 Lat. 1 Dep. ' Lat. Dep. ' Lat. 1 Dep. 0.94 0.34 0.94 0.35 0.94 0.35 0.94 i 0.35 2 1.88: 0.68 1.88 0.69 1.87 0.70 1.87 1 0.71 2 3 2.82 1.03 2.81 1.04 2.81 1.05 2.81; 1.06 3 4 3.76^ 1.37 ! 3.75 1.38 3.75 1.40 3.74 1.42 4 5 4.70i 1.71 1 4.69 1.73 , 4.68 1.75 4.68 1.77 5 6 5.64i 2.05 1 5.63 1 2.08 5.62 2.10 5.61 2.13 6 7 6.58; 2.39 : 6.57 2.42 ^ 6.56 2.45 6.55 2.48 7 8 7.52 2.74 : 7.51 2.77 7.49 2.80 7.48 1 2.83 8 9 8.46 3.08 8.44 3.12 8.43 3.15 8.42; 3.19 9 10 11 9.40 3,42 10.34 3.76 9.38 3.46 10,32; 3.81 9.37 3.50 9.35 3.54 : 10.29 ; 3,90 10 11 10.30 3.85 12 11. 2S 4.10 11.26 1 4.15 11.24 4.20 , 11.22 i 4.25 12 13 12.22 4.45 12.20 4.50 12.18| 4.55 12.16; 4.61 13 14 13.16 4.79 13.13 4.85 13.11! 4.90 13.09' 4.96 14 15 14.10 5.13 14.07 5.19 14.05 5.25 14.03 5.31 15 16 15.04^ 5.47 15.01 5.54 14.99 5.60 14.96 5.67 16 17 15.97, 5.81 15.95! 5.88 15.92 5.95 15.90: 6.02 17 18 16.911 6.16 16.89 1 6.23 16.86 6.30 16.83 6.38 18 19 17.85 1 6.50 17.83 1 6.58 17.80 6.65 17.77 6.73 19 20 18.79 6.84 18.76, 6.92 19.70 i 7.27, 18.73 1 7.00 19.67i 7.35 18.70' 7.09 20 21 21 19.73 7.18 19.64' 7.44 22 20,67. 7.52 20.64 i 7.61 20,61 : 7.70 20.57; 7.79 22 23, 21.61: 7.87 21.58: 7.96 21.54: 8.05 21.51^ 8.15 23 24 22.55! 8.21 22.52; 8.31 22.48: 8.40. 22.44 i 8.50 24 25 i 23.49 8.55 23.45! 8.65 23.42 1 8.76 23.38: 8.86 25 26: 24.43 8.89 24.39 1 9.00 24.35: 9.11 24.31 j 9.21 26 27 • 25.37 9.23 25.33! 9.35- 25.29' 9.46, 25.25: 9.57 27 28 26.31 9.58 26.27! 9.69; 26.23; 9.81 26.18. 9.92 28 29 27.25 9.92 27.21 10.04 27.16: 10.16 : 27.12; 10.27 29 30: 23.19 10.26 28.15:10.38 28.10 10.51 ' 28.05' 10.63 30 31 29.13 10.60 29.08, 10.73 29.04 10.86 28.99 10.98 31 32. 30.07 ]0.94 30.02, 11.08 29.97 11.21 i 29.92, 11.34 32 33 31.01 11.29 30.96 j 11.42} 3U.91 11.56 30.86] 11.69 33 34 31.95 11,63 31.90! 11.77; 31.85 11.91 i 31.79 1 12.05 34 35 32.89 11.97: 32.84; 12.11 : 32.78! 12.26 1 32.73! 12.40 35 36 33.83 12.31 33.77; 12.46 33.72: 12.61 ! 33.66 i 12.75 36 37 34.77 12.65 34.71 1 12.81 34.66; 12.96 34.60 j 13.11 37 38 . 35.71 13.00 35.65)13.15 35.59 1 13.31 35.54 13.46 38 39' 36.65 13.34 36..59; 13.50 36..53: 13.66 36.47 13.82 39 40 41 37.59 13.68 38,53 14.02 37.53 ! 13. S4 37.47 14.01 ! 38.47; 14. IP 3S.40 14.36; 37.41 14.17 40 41 38.34: 14.53 1 42 , 39.47 14.36 39 40; 14.. 54 39.34:14.71 39.28, 14.88 42 43 40.41 14.71 40.34:14.88 40.28 15.06 40.21 : 15.23 43 44 41.35 15.05! 41.28 115.23 41.21:15.41 41.15: 15.59 44 45 42.29 15.39 42.22 i 15.58 42.15 15.76 42.08 i 15.94 45 46, 43.23 15.73 ' 43.16 115.92 43.09.16.11 43.02; 16.30 46 47 44.17 16.07 44.09 i 16.27 44.02 i 16.46 43.95 16.65 1 47 48 45.11 16.42 45.03,16.61 44.96 i 16.81 44.89; 17.01 1 48 49 46.04 16.76 45.97' 16.96 45.90! 17.16 45.82 i 17.36 49 50 d II 46.98 17.10 La..| ^ i 46.91 17.31 46.83 1 Dep. 17.51 46.76! 17.71 50 1 Dep. Dep. Lat. i Lat. Dep. 1 Lat. 701 691 Deg. 69i Deg. 1 694 Deg. TRAVERSE TABLE. 43 20 Deg. 20i Deg. 20^ Deg. 201 Deg. 1 51 § - 51 Lat. Dep. Lat. Dep. 17.'65 Lat. 47.77 Dep. Lat. Dep. 47.92 17.44 47.85 17.86 47.69 18.07 52 48.86 17.79 48.79 18.00 48.71 18.21 48.63 18.42 52 53 49.80 18.13 49.72 18.34 49.64 18.56 49.56 18.78 53 54 50.74 18.47 50.66 18.69 50.58 18.91 50.50 19.13 54 55 51.68 18.81 51.60 19.04 51.52 19.26 51.43 19.49 55 56 52.62 19.15 1 52.54 19.38 52.45 19.61 52.37 19.84 56 57 53.56 19.50 53.48 19.73 53.39 19.96 53.30 20.19 57 58 54.50 19.84 54.42 20.07 54.33 20.31 54.24 20.55 58 59 55.44 20.18 55.35 20.42 55.26 20.66 55.17 20.90 59 60 61 56.38 20.. 52 56.29 20.77 56.20 21.01 56.11 21.28 60 61 57.32 20.86 57.23 21.11 57.14 21.36 57.04 21.61 62 58.26 21.21 58.17 21.46 58.07 21.71 57.98 21.97 62 63 59.29 21.55 59.11 21.81 59.01 22.08 58.91 22.32 63 64 60.14 21.89 60.04 22.15 59.95 22.41 59.85 22.67 64 65 61.08 22.23 60.98 22.50 60.88 22.76 60.78 23.03 65 66 62.02 22.57! 61.92 22.84 61.82 23.11 61.72 23.38 66 67 62.96 22.92 1 62.86 23.19 62.76 23.46 62.65 23.74 67 68 63.90 23.26 1 63.80 23.54 63.69 23.81 63.59 24.09 68 69 64.84 23.60; 64.74 23.88 64.63 24.16 64.52 24.45 69 70 71 65.78 66.72 23.94! 24.28 1 65.67 24.23 65.57 66.50 24.51 65.46 24.80 70 71 66.61 24.57 24.86 66.39 25.15 72 67.66 24.63 ! 67.55 24.92 67.44 25.21 67.33 25.51 72 73 68.60 24.97 68.49 25.27 68.38 25.57 68.26 25.86 73 74 69.54 25.31,', 69.43 25.61 69.31 25.92 69.20 26.22 74 75 70.48 25.65 70.36 25.96 70.25 26.27 70.14 26.57 75 76 71.42 25.99 71.30 26.30 71.19 26.62 71.07 26.93 76 77 72.36 26.34 72.24 26.65 72.12 26.97 72.01 27.28 77 78 73.30 26.68! 73.18 27.00 73.06 27.32 72.94 27.63 78 79 74.24 27.02! 74.12 27.34 74.00 27.67 173.88 27.99 79 80 81 75.18 27.36! 75.06 27.69 74.93 28.02 74.81 28.34 80 81 76.12 27.70 75.99 28.04 75.87 28.37 75.75 28.70 82 77.05 28.05 76.93 28.38 76.81 28.72 76.68 29.05 82 83 77.99 28.39 77.87 28.73 77.74 29.07 77.62 29.41 83 84 78.93 28.73 78.81 29.07 78.68 29.42 78.55 29.76 84 85 79.87 29.07 79.75 29.42 79.62 29.77 79.49 30.11 85 86 80.81 29.41 80.68 29.77 80.55 30.12 80.42 30.47 86 87 81.75 29.76 81.62 30.11 81.49 30.47 81.36 30.82 87 88 82.69 30.10 82.56 30.46 82.43 30.82 82.29 31.18 8S 89 83.63 30.44 83.50 30.80 83.36 31.17 83.23 31.53 89 90 91 84.57 30.78 84.44 31.15 84.30 31.52 84.16 31.89 32.24 90 91 85.51 31.12 85.38 31.50 85.24 31.87 85.10 92 86.45 31.47 86.31 31.84 86.17 32.22 86.03 32.59 92 93 87.39 31.81 87.25 32.19 87.11 32.57 86.97 32.95 93 94 88.33 32.15 88.19 32.54 88.05 32.92 87.90 33.30 94 95 89.27 32.49 89.13 32.88 88.98 33.27 88.84 33.66 95 96 90.21 32.83 90.07 33.23 89.92 33.62 89.77 34.01 96 97 91.15 33.18 91.00 33.57 90.86 33.97 90.71 34.37 97 98 92.09 33.52 91.94 33.92 91.79 34.32 91.64 34.72 98 93 93.03 33.86 92.88 34.27 92.73 34.67 92.58 35.07 99 100 .2 Q 93.97 34.20 93.82 34.61 93.67 35.02 93.51 35.43 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 70 Deg. 691 Deg. 69i Deg. 69i Deg. ll 44 TRAVERSE TABLE. B 21 1'! Deg. 214 Deg. ji 2a Deg. i }! Lat. j Dep. Ij 211 Deg. zi '1 1" i Lat. 1 Dep. Lat. Dep. :j Lat 1 Dep. j § 1 0.93 1 0.36' 0.93 0.36 J! 0.93 0.37 ! 0.93 0..37! 1 2 1.87 ■ 0.72 1.86 0.72 -j 1.86 0.73 J 1.36 0.74' 2 3! 2.80 1.08: 3.80 1.09 Ii 2.79 1.10 i 2.79 1.11 3 4 1 3.73 ' 1.43 3.73 1.45 ll 3.72) 1.47 ! 3.72 1.48 i 4 5! 4.67 1.79 4.66 1.81 II 4.65i 1.83 1 4.64 1.85 i 5 6l 5.60 , 2.15 5.59 2.17 ! 5.58 i 3.20 i 5.57 2.22 6 7 1 6.54 2.51 ! 6.52 2.54 i 6.51 ! 2.57 i 6.50; 2.59 7 8! 7.47 2.87 i 7.46 2.90 i 7.44 i 2.93 ! 7.43 2.96 8 9; 8.40 3.23 8.39 3.26 j 8.37 1 3.30 ! 8.36 3.34 9 10 I 9.34 11 : 10.27 3.5S 9.32 3.62 ; 9.30' 3.67 9.29 3.71 10 j 10.22 4.08 11 3.94 10.25 3.99 110.23 4.03 12 : 11.20 4.30 11.18 4.35 i 11.17 4.40 11.15; 4.45. 12 13 ■. 12.14 4.66 12.12 4.71 113.10 4.76 ! 12.07' 4.82 ' 13 14! 13.07 5.02 13.05 5.07 13.03 j 5.13 i 13.00 5.19 14 15 14.00 5.38 13.98 5.44 ' 13.96! 5.50 13.93 5.56 15 16 14.94 5.73 : 14.91 5.80 ; 14.89 1 5.86 ; 14.86 5.93 16 17' 15.87 6.09 15.84 6.16 '■ 15.32; 6.23 I 15.79' 6.30 i 17 18-16.80 6.45 16.73 6.52 ; 16.75 i 6.60 1 16.72 6.67 , 18 19 : 17.74 6.81 17.71 6.89 ! 17.68 ! 6.96 ! 17.65 7.04 19 2,0 18.67 7.17 13.64 19.57 7.25 7.61 IS. 61 ; 7.33 18.53 7.41 20 19.54. 7.70 ; 19.50 7.78 21 21 19.61 7.53 22 20.54 7.88 20.50 7.97 ; 20.47 1 8.06 20.43 8.15 23 23 21.47 8.24 21.44 8.34 ■21.40! 8.43 121.36; 8.52 23 24 22.41 8.60 i 22.37 8.70 22.33: 8.80 i 22.39' 8.89 34 25 23.34 8.96 : 23.30 9.06 23.26 9.16 i 23.22 9.26 35 26 24.27 9.32 , 24.23 9.42 24.19' 9.53 24.15; 9.63 26 27 25.21 9.SS : 25.16 9.79 .25.12^ 9.90 25.08 10.01 ! 27 2S . 26.14 10.03 ' 26.10. 10.15 26.05 10.26 26.01 10.38 , 23 29 . 27.07 10.39 27.03 10.51 26.98 10.63 36.94 ' 10.75 ' 29 30 2S.01 31 ,28.94 10.75 11.11 > 27.96 28.89 10.87 11.24 ! 27.91 11.00 '23.84; 11.36 27.86 11.12 30 28.79 11.49; 31 32 : 29.87 11.47 29.82 11.60 29.77 ; 11.73 29.72 11.86 I 32 33 '30.81 11.83 30.76 11.96 30.70; 12.09 30.65 12.23 , 33 34 ' 31 . 74 12.18: 31.69 12.32 31.63 12.46 31.53 12.60 .34 35 '32.68 12.54 1 32.62 12.69 32.56 12.83 32.51 12.97 35 36 133.61 12.90*; 33.55 13.05 33.50 13.19 33.44 13.34 36 37 34.54 13.26 ii 34.48 13.41 ' 34.43 i 13.56 34.37 13.71 37 33 : 35. 4S 13.62 i| 35.42 13.77 35.36 13.93 35.29 14.08 33 39 ! 36.41 13. 9S i 36.35 14.14. 36.29 14.29 36.22 14.45 39 40 1 37.34 14.33 i 37.28 14.50 37.22 14.66 37.15 14.82 ' 40 41 !3S.2S 14.69 ' 38.21 14.86 f 33.15 15.03 33.03 15.19 41 42 '39.21 15.05 i 39.14 , 15.22 i 39.08 15.39 39.01 15.56 42 43 UO.14 15.41 i 40.08 : 15.58 40.01 15.76 : 39.94 15.93 i 43 44 : 41.08 15.77 ' 41.01 : 15.95 40.94 16.13 ' 40.87 16.30 ; 44 45 = 42.01 16.13 ! 41.94^ 16.31 ■ 41.87 16.49 41.80 16.68 ': 45 46 42.94 16.48 i 42.87 ■ 16.67 42.80 16.86 42.73 17.05 ! 46 47 43.88- 16.84 ■! 43.80 17.03 ; 43.73 17.23 43.65 : 17.42 1 47 4S 44.81 17.20 ■ 44.74 17.40 ; 44.66 17.59 44.58 17.79; 4^ 49 145.75 17.56 45.67 17.76 i 45.59 17.96 45.51 ■ 18.16 ! 49 50 1 46.68 17.92 ! 46 . 60 : 18.12 i 46.52 18.33 46.44! 18.53 50 1 Dep. , Lat. i Dep. i Lat. Dep. j Lat. Dep. ! Lat. | | Q 69 Deg. ij i ^1 1 681 Deg. 681 Deg. 684 Deg. i i TRAVERSE TABLE. 45 f- 51 ' 21 Deg. 2H Deg. 2H Deg. 1 211 Deg. 1 51 Lat. Dep. Lat. 47.53 Dep. Lat. Dep. Lat. Dep. 47.61 18.28 18.48 47.45 18.69 47.37 18.90 52 48.55 18.64 48.46 18.85 48.38 19.06 48.30 19.27 52 53 49.48 18.99 49.40 19.21 49.31 19.42 49.23 19.64 53 54 50.41 19.35 50.33 19.57 50.24 19.79 50.16 20.01 54 55 51.35 19.71 51.26 19.93 51.17 20.16 51.08 20.38 55 56 52.28 20.07 52.19 20.30 52.10 20.52 52.01 20.75 56 57 53.21 20.43 53.12 20.66 53.03 20.89 52.94 21.12 57 58 54.15 20.79 54.06 21.02 53.96 21.26 53.87 21.49 58 59 55.08 21.14 54.99 21.38 54.89 21.62 54.80 21.86 59 60 61 56.01 21.50 55.92 21.75 55.83 21.99 1 55.73 56.66 22.23 60 61 56.95 21.86 56.85 22.11 56.76 22.36 ! 22.60 62 57.88 22.22 57.78 22.47 57.69 22.72 1 57.59 22.97 62 63 58.82 22.58 58.72 22.83 58.62 23.09 1 58.52 23.35 63 64 59.75 22.94 59.65 23.20 59.55 23.46 1169.44 23.72 64 65 60.68 23.29 60.58 23.56 80.48 23.82 li 60.37 24.09 65 66 61.62 23.65 61.51 23.92 61.41 24.19 11 61.30 24.46 66 67 62.55 24.01 62.44 24.28 62.34 24.56 !' 62.23 24.83 67 68 63.48 24.37 63.38 24.65 63.27 24.92 I 63.16 25.20 68 69 64.42 24.73 64.31 25.01 64.20 25.29 i 64.09 25.57 69 70 71 65.35 25.09 65.24 25.37 ,65.13 25.66 i 65.02 25.94 70 71 66.28 25.44 i 66.17 25.73 166.06 28.02 1 65.95 26.31 72 67.22 25.80 jl 67.10 1 26.10 66.99 26.39: 66.87 26.68 72 73 68.15 26.16 i 68.04 26.46 167.92 26.75 : 67.80 27.05 73 74 69.08 26.52 68.97 26.82 68.85 27.12, 68.73 27.42 74 75 70.02 26.88 69.90 27.18 69.78 27.49 1 69.66 27.79 75 76 70.95 27.24 70.83 27.55 70.71 27.85 1 70.59 28.16 76 77 71.89 27.59 71.76 27.91 71.64 28.22 i 71.52 28.53 77 78 72.82 27.95 72.70 28.27 172.57 28.59 1 72.45 28.90 78 79 73.75 28.31 73.63 28.63 i 73.50 28.95 73.38 29.27 79 80 81 74.69 28.67 29.03 74.56 75.49 29.00 29.36 74.43 29.32 29.69 74.30 29.64 80 81 75.62 75.36 75.23 30.02 82 76.55 29.39 76.42 29.72 1 76.29 30.05 76.16 30.39 82 83 77.49 29.74 77.36 30.08 i 77.22 30.42 77.09 30.76 83 84 78.42 30.10 78.29 30.44 ! 78.16 30.79 78.02 31.13 84 85 79.35 30.46 79.22 30.81 il 79.09 31.15 178.95 31.50 85 86 80.29 30.82 80.15 31.17 180.02 31.52 1179.88 31.87 86 87 81.22 31.18 81.08 31.53 ii 80.95 31.89 1180.81 32.24 87 88 82.16 31.54 82.02 31.89 i 81.88 32.25 181.74 32.61 88 89 83.09 31.89 82.95 32.26 82.81 32.62 182.66 32.98 89 90 91 84.02 32.25 83.88 32.62 1 83.74 32.99 1 83.59 33.35 90 84.96 32.61 84.81 32.98 i'l 84.67 33.35 84.52 33.72 91 92 85.89 32.97 85.74 33.34 1 85.60 33.72 85.45 34.09 92 93 86.82 33.33 86.68 33.71 ' 86.. 53 34.08 86.38 34.46 93 94 87.76 33.69 87.61 34.07 87.46 34.45 87.31 34.83 94 95 88.69 34.04 88.54 34.43 88.39 34.82 88.24 35.20 95 96 89.62 34.40 89.47 34.79 89.32 35.18 89.17 35.57 96 97 90.56 34.76 90.40 35.16 90.25 35.55 90.09 35.94 97 98 91.49 35.12 91.34 35.52 91.18 35.92 91.02 36.31 98 99 92.42 35.48 92.27 35.88 92.11 36.28 91.95 36.69 99 100 93.36 35.84 93.20 36.24 93.04 36.65 92.88 37.06 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. B " 1 5 69 Deg. 681 Deg. 68i Deg. 68i Deg. 4G TBJtVEESZ TABLE. ?. I 1 2 3 4 5 6 9! 10 ; 11 1 12 i 13 I 14! 15 I }?! 13 19! 20 ! 22 D6g. j; 1; Lat. Dep. r 0.93 0.37 i I. So 0.75 i 2.78 1.12 3.71 1.50 4.64 1.87 5.56 2.25 6.49 2.62 7.42 3.00 1 8.34 3.37 1 9.27 3.75 i 22i Des. 22k Deg. I 2 Lat. Dep. j Lat. '■ Dep. Lat. 0.93 1.85 2.78 3.70 4.63 5.55 6.48 7.40 8.33 9.26 10.20 11.13 12.05 12.98 13.91 14.83 15.76 16.69 17.62 18.54 4.12 4.50 4.87 5.24 5.62 5.99 6.37 6.74 7.12 7.49 I; 10.18 11.11 12.03 12.96 13.88 14.81 15.73 I 16.66! 17.. 59 i 18.51 i 0.38 0.76 1.14 1.51 1.89 2.27 2.65 3.03 3.41 3.79 4.17 4.54 4.92 5.30 5.68 6.06 6.44 6.82 7.19 7.57 Dep. I 0.92 1 1.85 1 2.77 I 3.70 1 4.62 1 5.541 6.47! 7.39 1 8.31 I 9.24 0.38 0.77 1.15 1.53 1.91 2.30 2.68 3.06 3.44 3.83 4.21 4.59 4.97 5.36 5.74 6.12 6.51 6.89 7.27 7.65 0.92! 1.84, 2.77 3.69 1 4.61 I 5.53 6.46 7.38 8.30 9.22 0.39 0.77 1.16 1.55 1.93 1 2.32 2.71 I 3.09 i 3.48 3.87 1 » 3 4 5 6 7 8 9 10 14 07 99 91 83 76 68 i 60 I 52 I 44 4.25 4.64 5.03 5.41 5.80 6.19 6.57 6.96 7.35 7.73 11 12 13 14 15 16 17 18 19 20 21 19.47 ! 22 i 20.40 i 23! 21.33; 24 I 22.25 I 25 I 23.18 26 i 24.11 I 27 125.03 1 28 ■ 25.96 j 26.89 i 27.82 ! 30 7.87 8.24 8.62 11 8.99 II 9. .37 9,74! 10.11 [! 10.49 11 10.86!' 11.24|i 19.44 20.36 21.29 22.21 23. li 24.06 24.99 25.92 26.84 27.77 31 ! 28.74 ; 32 129.67 ! 33 130.60; 34 31.52: 35 32.45 I 36 33.38 j 37 34.31 I 38 35.23 j 39 I 36.16 j 40 87 . 09 I 11.61 ; 11.99 li 12.36 |i 12.74 I 13.11 li 13.49 |i 13.86 1! 14.24!; 14.61 if 14.98 !i 28.69 .. 29.62 . 30.54, 31.47 I 33.39 1 33.32 34.24 1 35.17! 36.10 37.02 7.95 8.33 8.71 9.09 9.47 9.84 10.22 10.60 iO.98 11.36 ! 27, 11.74 1 28, 12.12 j 29. ,40 ,33 .25 .17 ,10 ,02! ,94 ' ,87 j ,79 I ,72 i 8.04:1 19 8.42 20 8.S0 21 9.1s 22 9.57 23 9.951; 23 10.33; 24 10.72 1 25 ll.l0i!26 11.48 27 ,37] ,29 i .21 i ,131 ,05 ! ,98 10.05 1 90 10.44 82 j 10.83 74! 11.21 67 ! 1 1 . 60 8.12 8.51 ; 8.89 I 9.28 i 9.6-' 21 22 23 24 25 26 27 28 29 30 4-: 3S,94 43; 39.87 44 i 40.80 45! 41.72 46 42.65 47 43.58 48 44.50 49 45.43 50 46.36 15.36 15.73 16.11 16.48 16.86 17.23 17.61 17.93 18.36 18.73 37.95 ._38.87 39.80 40.72 41.65 42.57 43.50 44.43 ■' 45.35 :i 46.28 12.50': 30 12.87;! 31 13.25' .32 13.63 i 33 14.01 ! 34 14.39' 35 14.77'! 36 15 1=; I ?K 64' 56; 49! 41 I 34 26 18 1 11! 03 I 1 f .86 12.25 ■ 12.63 ; 13.01 13.39 I 13.78 ii 14.16 ' 14. .54! 14.92 !; 15.31 I 59! 11.99! 51 i 12.37; 43 i 12.76! 35! 13.15 28 I 13.53 20 I 13.92 12 1 14.31 04! 14.70 97 j 15.08 89 I 15.47 39.73 40.65 41.57 15.:, 15.9: 16.28 16.65 17.04 17.42 i 42.50 17.80 ii 43.42 18.18 ^i 44.35 18.55 ! 45.27 18.93 ;| 46.19 § ' Dep. Lat. li Dep. | Lat. ! Dep. Lat. ;; Dep. Lat. 15. b9 ;37 16.07 1; 38 16.46; -39 16.84 1 40 17.22 i! 41 17.60 42 17.99 43 18.37; 44 18.75 45 19.13 i 46 .81! .73 1 .65 1 .58 .50 .42 .34 .27 .19 .11 15.86 16.24 16.63 17.02 17.40 17.79 18.18 18.56 13.95 19.34 Deg. H 67i De^. 6Ti Def. 1 67i Deg. 31 32 33 .34 35 36 37 38 39 40 41 42 43 44 4.'i 46 47 48 49 50 TRAVERSE TABLE. 47 o K 3 o CD "51 22 Deg. 22i Deg. 22^ Deg. 221 Deg. w p ? 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 47.29 19.10 47.20 19.31 47.12 19.52 47.03 19.72 52 48.21 19.48 48.13 19.69 48.04 19.90 47.95 20.11 52 53 49.14 19.85 49.05 20.07 48.97 20.28 48.88 20.50 53 54 50.07 20.23 49.98 20.45 49.89 20.66 49.80 20.88 54 55 51.00 20.60 50.90 20,83 50.81 21.05 .50.72 21.27 55 56 51.92 20.98 51.83 21.20 51.74 21.43 51.64 21.66 56 57 52.85 21.35 52.76 21.58 .52.66 21.81 52.57 22.04 57 58 53.78 21.73 53.68 21.96 53.59 22.20 53.49 22.43 58 59 54.70 22.10 54.61 22.34 54.51 22.58 54.41 22.82 59 60 61 55.63 22.48 55.53 22.72 55.43 22.96 55.33 23.20 60 61 56.56 22.85 56.47 23.10 56.36 23.34 56.25 23.59 62 57.49 23.23 57.38 23.48 57.28 23.73 57.18 23.98 62 63 58.41 23.60 58.31 23.85 58.20 24.11 58.10 24.36 63 64 59.34 23.97 59.23 24.23 59.13 24.49 59.02 24.75 64 65 60.27 24.35 60.16 24.61 60.05 24.87 59.94 25.14 65 66 61.19 24.72 61.09 24.99 60.98 25.26 60.87 25.52 66 67 62.12 25.10 62.01 25.37 61.90 25.64 61.79 25.91 67 68 63.05 25.47 62.94 25.75 62.82 26.02 62.71 26.30 68 69 63.98 25.85 63.86 26.13 63.75 26.41 63.63 26.68 69 70 71 64.90 26.22 64.79 26.51 64.67 26.79 64.55 27.07 70 71 65.83 26.60 65.71 26.88 65.60 27.17 65.48 27.46 72 66.76 26.97 66.64 27.26 66.52 27.55 66.40 27.84 72 73 67.68 27.35 67.56 27.64 67.44 27.94 67.32 28.23 73 74 68.61 27.72 68.49 28.02 68.37 28.32 68.24 28.62 74 75 69.54 28.10 69.42 28.40 69.29 28.70 69.17 29.00 75 76 70.47 28.47 70.34 28.78 70.21 29.08 70.09 29.39 76 77 71.39 28.84 71.27 29.16 71.14 29.47 71.01 29.78 77 78 72.32 29.22 72.19 29.53 72.06 29.85 71.93 30.16 78 79 73.35 29.59 73.12 29.91 72.99 30.23 72.85 30.55 79 80 81 74.17 29.97 74.04 30.29 73.91 30.61 73.78 30.94 80 81 75.10 30.34 74.97 30.67 74.83 31.00 74.70 31.32 82 76.03 30.72 75.89 31.05 75.76 31.38 75.62 31.71 82 83 76.96 31.09 76.82 31.43 76.68 31.76 76.54 32.10 •83 84 77.88 31.47 77.75 31.81 77.61 32.15 77.46 32.48 84 85 78.81 31.84 78.67 32.19 78.53 32.53 78.39 32.87 85 86 79.74 32.22 79.60 32.56 79.45 32.91 79.31 33.26 86 87 80.66 32.59 80.52 32.94 80.38 33.29 80.23 33.64 87 88 81.59 32.97 81.45 33.32 81.30 33.68 81.15 34.03 88 S9 82.52 33.34 82.37 33.70 82.23 34.06 82.08 34.42 89 90 91 83.45 33.71 83.30 34.08 83.15 34.44 83.00 34.80 90 91 84.37 34.09 84.22 34.46 84.07 34.82 83.92 36.19 92 85.30 34.46 85.15 34.84 85.00 35.21 84.84 35.58 92 93 86.23 34.84 86.08 35.21 85.92 35.59 85.76 35.96 93 94 87.16 35.21 87.00 35.59 86.84 35.97 86.69 36.35 94 95 88.08 35.59 87.93 35.97 87.77 36.35 87.61 36.74 95 96 89.01 35.96 88.85 36.35 88.69 36.74 88.53 37.12 96 97 89.94 36.34 89.78 36.73 89.62 37.12 89.45 37.51 97 98 90.86 36.71 90.70 37.11 90.54 37.50 90.38 37.90 98 99 91.79 37.09 91.63 37.49 91.46 37.89 91.30 38.28 99 100 1 to 5 92.72 37.46 92.55 37.86 92.39 38.27 92.22 38.67 100 6 o a Q Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 68 Deg. 67| Deg. 67i Deg. 67i Deg. 48 THAVEESr. TXBLr. Cl 23 Deg. ' 23+ Deg. 1 2^ Deg. : 231 Deg. c 1 1 ; ^-at. Dep. : Lat. Dep. Lat. Dep. |; Lat. Dep. 1. 0.92 0.39, 0,92 0.39 0.92 0.40 0.92 0.40 2 1.84 0.78'; 1.84 0.79 1.83 0.80 1.83 0.81 2 3 1 2.76 1.17;, 2.76 1.19 2.75 1.30 2.75 1.21 3 4! 3.68 1.56' 3.68 1.58 3.67 1.59; 3.66 1.61 4 5! 4.60 1.95 4.59 1.97 4.59 1.99 4.58 2.01 5 6 ' 5.52 2.34 5.51 2.37 5.50 2.39 5.49 2.42 6 7 i 6.44 2.74 6.43 2.76 6.42 2.79 6.41 2.82 7 8i 7.36 3.13 7.35 3.16 1 7.34 3.19 7.32 3.22 8 9: 8.2s 3.52 8.27 3.551 8.25 3.59 8.24 3.62 9 10 9.20 11 10.13 3.91 9.19 4.30 ; 10.11 3.95 1 4.34 ( 9.17 10.09 3.99 9.15 4.03 10 11 4.39 10.07 4.43 12 11.05 4.69 11.03 4.74 ! 11.00 4.78 10.98 4.83 12 13 i 11.97 5.08 ; 11.94 5.13 1 11.92 5.18 11.90 5.24 13 14; 12.89 5.47 1 12.86 5.53 12.84 5.58 12.81 5.64 14 15 13.81 5.86 ; 13.78 5.92 13.76 5.98 13.73 6.04 15 16 14.73 6.25 14.70 6.32 14.67 6.38 14.64 6.44 16 17 15.65 6.64; 15.62 6.71 15.59 6.78 15.56 6.85 17 18 16.57 7.03 ; 16.54 7.11 7.50 16.51 7.18 16.48 7.25 18 19 : 17.49 7.42 L 17.46 7.81 f 18.38 17.42 7.58 17.39 7.65 19 20' 18.41 7.89 ' 18.34 7.97 18.31 8.05 20 21 19.33 I 8.21 1 19.29 8.29 19.26 8.37 19.22 8.46 21 22 20.25 8.60 20.21 , 8.68 20.18 8.77 1^20.14 8.86 22 23 21.17 . 8.99 ! 21.13 1 9.08 21.09 9.17 =21.05 9.26 23 24 122.09 ^ 9.38 22.05 1 9.47 22.01 9.57 ; 21.97 9.67 24 25 23.01 ' 9.77 22.97 , 9.87 22.93 9.97 '22.88 10.07 25 26 23.93 10.16 23.89 10.26 23.84 10.37 23.80 1 10.47 26 27 24.85 ; 10.55 24.81 ; 10.66 24.76 10.77 24.71 10.87 27 28 25.77 10.94 25.73 j 11.05 125.68 11.16 25.63 11.28 28 29 ,26.69 11.33 26.64 ' 11.45 26.59 11.56 26.54 ; 11.68 29 30 27.62 11.72 27.56 '; 11.84 27.51 11.96 27.46 12.36 28.37 ' 12.08 30 31 28.. 54 12.11 28.48 ; 12.24 28.43 , 12.49 31 32 29.46 12.50 29.40 12.63 29.35 12.76 29.29 12.89 32 33.30.38 12.89 30.32 13.03 30.26 13.16 30.21 ■: 13.29 33 34 31.30 13.28 . 31.24 '■: 13.42 31.18 13.56 31.12 13.69 34 35 32.22 13.68 : 32.16 13.82 : 32 . 10 . 13.96 32.04 ; 14.10 35 36 33.14 14.07 33.08 14.21 33.01 : 14.35 32.95 14.50 36 37 .34.06 14.46 34.00 14.61 33.93 ■ 14.75 33.87 14.90 37 33 ; 34.98 14.85 34.91 , 15.00 ; 34.85 15.15 : 34.78 15.30 38 39 35.90 15.24 35.83 15.39 35.77 15.55! 35.70 15.71 39 40 36.82 15.63 36.75 15.79 36.68 15.95 : 36.61 '■: 16.11 40 41 37.74 16.02 37.67 16.18 37.60 16.35 i 37.. 53 16.51 41 42 38.66 16.41 38.59 16. 5S 38.. 52 16-75 3S.44 16.92 42 43 39.58 16.80 39.51 16.97 39.43 17.15 J 39.36 ; 17.32 43 44:40.50 17.19 40.43 17.37 40.35 17.54 40.27 17.72 44 45 '41.42 17. .58 41.35 17.70 41.27 17.94< 41.19 18.12 45 46 42.34 17.97 42.26 18.16 142.18 18.34 ; 42.10 19.53 46 47 43.26 18.36 43.18 18.55 43.10 18.74 43.02 18.93 47 48 44.18 18.76 44.10 18.95 44.02 19.14 43.93 19.33 4H 49 45.10 19.15 45.02 19.34 44.94 19.54 44.85 (19.73 49 50 46.03 19.54 45.94 19.74 45.85 19.94 45.77 20.14 1 50 § ; Dep. 1 ; Lat. Dep. Deg. ;: 661 Lat. Dep. Lat. Dep. : Lat. 1 s J Deg. 66^ Deg. i, 66i Deg. TKA\£RSE TABLE. 4'd p 3 51 23 Deg. 23i Deg. 23f Deg. 231 Deg. 3 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 46.95 19.93 46.86 20. 13 46.77 20.34 46.68 20.54 51 52 47.87 20.33 47.78 20 53 47.69 20.73 47.60 20.94 52 53 48.79 20.71 48.70 20.92 48.60 31.13 48.51 21.35 53 54 49.71 21.10 49.61 21.32 49.52 21.53 49.43 21.75 54 55 50.63 21.49 50.53 21.71 50.44 21.93 50.34 22.15 55 56 51.55 21.88 51.45 22.11 51.36 22.33 51.26 22.55 56 57 52.47 22.27 53.37 22.50 52.27 33.73 52.17 22.96 57 58 53.39 22.66 53.39 22.90 53.19 33.13 53.09 23.36 58 59 54.31 23.05 54.31 23.29 54.11 23.53 54.00 33.76 59 60 61 55.23 23.44 23.83 55.13 23.68 55.02 23.92 54.93 55.83 24.16 24.57 60 61 56.15 56.05 24.08 55.94 24.33 62 57.07 24.23 56.97 24.47 56.86 24.72 56.75 24.97 62 63 57.99 24.63 57.88 34.87 57.77 25.12 57.66 25.37 63 64 58.91 25.01 .58.80 25.26 58.69 25.52 58.58 25.78 64 65 159.83 25.40 59 . 72 25.66 59.61 25.92 159.50 26.18 65 66 60.75 25.79 60.64 26.05 60.53 26.32 1 60.41 26.. 58 66 67 61.67 26.18 61.56 26.45 61.44 26.73 ! 61.33 28.98 67 68 62.59 26 . 57 62.48 36.84 62.. 38 63.2^ 37.11 62.24 127.39 68 69 63.51 26.96 63.40 37.24 37.51 63.16 27.79 69 70 71 64.44 27.35 64.32 27.63 64.19 37.91 28.31 64.07 64.99 28.19 70 65.36 27.74 65.23 28.03 65.11 28.59 71 72 66.28 28.13 66.15 28.42 66.03 28.71 65.90 29.00 73 73 67.20 28.52 67.07 28.82 66.95 29.11 66.82 29.40 73 74 ,68.12 28.91 67.99 29.21 67.86 39.51 67.73 29.80 74 75! 69.04 29.30 68.91 29.61 68.78 29.91 68.65 30.21 75 76 69.96 29.70 69.83 30.00 69.70 30.30 69.56 30.61 76 77 70.88 30.09 70.75 30.40 70.61 30.70 70.48 31.01 77 78 71.80 30.48 71.67 30.79 71.53 31.10 71.39 31.41 78 79 72.72 30.87 72.58 31.18 72.45 31.50 72.31 31.82 79 80 81 73.64 31.26 73.50 31.58 73.36 31.90 73.22 32 . 22 80 81 74.56 31.65 74.42 31.97 74.28 32.30 74.14 32.63 82 75.48 32.04 75.34 32.37 75.20 33.70 75.06 33.03 82 83 76.40 32.43 76.26 32.76 76.12 33.10 75.97 33.43 83 84 77.32 32.82 77.18 33.16 77.03 33.49 76.89 33.83 84 85 78.24 33.21 78.10 33,55 77.95 33.89 77.80 34.23 85 86 79.16 33.60 79.02 33.95 78.87 34.29 78.72 34.64 86 87 80.08 33.99 79.93 34.34 79.78 34.69 79.63 35.04 87 88 81.00 34.38 80.85 34.74 80.70 .35.09 80.55 35.44 88 89 81.92 34.78 81.77 35.13 81.62 35.49 81.46 35.84 89 90 91 82.85 35.17 82.69 83.61 35.53 82.54 35. S9 82.38 36.25 90 83.77 35.56 35.92 83.45 36.29 1 83.29 36.65 91 92 84.69 35.95 84.. 53 36.33 84.37 36.68 84.21 37.05 92 93 85.61 36.34 85.45 36.71 85.29 37.08 1 85.13 37.46 93 94 86.53 36.73 86.37 37.11 80.20 i 37.48 . 86.04 .37.86 94 95 87.45 37.12 87.29 37.50 1 87.12 37.88 86.95 38.26 95 96 88.37! 37.51 88.20 37.90 88.04 38.28 ! 87.87 38.66 96 97 89.29 137.90 89.12 38.39 88.95 38.68 88.79 39.07 97 98 90.21 138.29 90.04 38.68 1 89.87 39.08 89.70 39.47 98 99 91. 13 138.68 90.96 39.08 90 . 79 i 39.48! 90.62 39.87 99 100 d .2 1 L 92.05 i. 39. 07 91.88 39.47 91.71 39.87 1 91.53 40.27 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. o a a 67 Deg. 1 661 Deg. 661 Deg. 664 Deg. 60 TRAVEBSE TABLE. 24] Deg. m Deg, 1 24|Deg. 24J Deg. 1 a ~1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 Dep. 0.91 0.41 0.91 0.41 i 0.91 0.41 0.91 1 0.42 2 1.83 0.81 1.82 0.82 11 1.82 0.83 1.82 0.84 2 3 2.74 1.22 2.74 1.23 i! 2.73 i 1.24 2.72 i 1.26 3 4 3.65 1.63 3.65 1.64! 3.64! 1.66 3.63; 1.67 4 5 4,67 2.03 4.56 2.05 ij 4.55! 2.07 4.54 1 2.09 5 6 5.-18 2.44 II 5.47 2.46 1! 5.46 2.49 5.45 j 2.51 6 7 6.39 2.85 6.38 2.87 j 6.37 2.90 6.36 2.93 7 8 7.31 3.25 7.29 3.29 1 7.28 3.32 7.27 3.35 8 9 8.22 3.66 8.21 3.70! 8.19 3.73 8.17 3.77 9 10 9.14 11 1 10.05 4.07 1 4.47 1 9.12 4.11 9.10 10.01 4.15 9.08 ' 4.19 10 11 10.03 4.52 4.56 9.99 i 4.61 12 1 10.96 4.88 1 10.94 4.93 1! 10.92 4.98! 10.90 1 5.02 12 13 j 11.88 5.29 !| 11.85 5.34!! 11.83 5.39 11.81 5.44 13 14! 12.79 5.69 1 12.76 6.10 13.68 6.51 ij 14.59 5.75 { 12.74 5.81 12.71! 5.86 14 15 1 13.70 6.16 13.65 6.221 13.62 1 6.28 15 16 1 14.62 6.57 1 14.56 i 6.641 14.53 6.70 16 17 ; 15.53 6.92 Ij 15.50 6.98 !l 15.47 i 7.05 15.44 7.12 17 18 16.44 7.32 16.41 7.39,116.38 1 7.46 1 t.SO!! 17.29 1 7.88 1 16.35 7.54 18 19 117.36 7.73 ii 17.32 17.25 1 7.95 19 20 18.27 21 1 19.18 8.131 18.24 8.21 I 18.20 1 8.29 18.16 1 8.37 20 21 8.54^ 19.15 8.63 19.11 i 8.71 19.07 8.79 22 '20.10 8.95 20.06 9.04 20.02 i 9.12! 19.98 9.21 22 23 1 21.01 9.35, 20.97 9.45 20.93 9.54 20.89 9.63 23 24! 21.93 9.76 ,21.88 9.86 21.84 9.95: 21.80 10.05 24 25 j 22.84 10.17 22.79 10.27 j 22.75 10.37 i 22.70 10.47 25 26 23.75 10.58 23.71 10.68 23.66 10.78 1 23.61 1 10.89 26 27 24.67 10.98 1 24.62 11.09,1 24.57 11.20 24.52 ' 11. .30 27 28 25.. 58 11.39 1 25.53 11. .50 25.48 11.61 25.43 1 11.72 28 29 j 26.49 11.80 26.44 11.91 (1 26.39 12.03 26.34! 12.14 29 30 31 27.41 12.20 27.35 12.32 Ij 27.30 12.44 27.24! 12.56 28.15 i 12.98 30 31 28.32 12.61 i 28.26 12.73!! 28.21 12.86 32 29.23 13.02 29.18 13.14!j 29.12 13.27 29.06 1 13.40 32 33 30.15 13.42 30.09 13.55 11 30.03 13.68 29.97 j 13.82 33 34 31.06 13.83 31.00 13.96 1 30.94 14.10 30.88 i 14.23 34 35 31.97 14.24 31.91 14.38 jl 31.85 14.51 31.78 i 14.65 35 36 132.89 14.84 1 32.82 14.79 1132.76 14.93. 32.69 ; 15.07 36 37 133.80 15.05 1 33.74 15.20 1 33.67 15.34! 33.60 1 15.49 37 38 134.71 15.46 34.65 15.61 H 34.58! 15.76 34.51 i 15.91 38 39 i 35.63 15.86 35.56 16.02 '35.49 16.17 35.42 i 16.33 39 40!. 36. 54 41 i 37.46 16.27 16.68 ■ 36.47 16.43 36.40 16.59 36.33 ! 16.75 40 41 37.38 16.84 ii 37.31 ! 17.00 1 37.23 ; 17.16 42 138.37 17.08 38.29 17.25 |! 38.22 i 17.42 38.14! 17.. 58 42 43 139.28 17.49 39.21 17.66 1| 39.13 17.83 39.05 18.00 43 44 40.20 17.90 40.12 18.07 !l 40.04 18.25 39.96 i 18.42 44 45 41.11 18.30 41.03 18.48 ;[ 40.95 1 18.66! 40.87 1 18.84 45 46 42.02 18.71 41.94 18.89: 41.86 ; 19.08 41.77; 19.26 46 47 42.94 19.12 ' 42.85 19.30 42.77 1 19.49 42.68 i 19.68 47 48 43.85 19.52 43.76 19.71i 43.68 i 19.91 43.59 120.10 48 49 44.76 19.93 44.68 20.13! 44.59 20.32 44.50 120.51 49 JO 45.68 20.34 Lat. I 45.59 20.54! 45.50 20.73 1 45.41 ! 20.93 50 1 Dep. Dep. 651 Lat. Deg. Dep. Lat. Dep. 1 Lat. 1 66] 3eg. 65i Deg. 65^ Deg. TRAVERSE TABLE. 51 i "51 24Deg. 24i Deg. 24i Deg. 24| Deg. O 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 46.59 20.74 46.50 20.95 46.41 21.15 46.32 21.35 52 47.50 21.15 47.41 21.36 47.32 21.56 47.22 21.77 52 53 48.42 21.56 48.32 21.77 48.23 21.98 48.13 22.19 53 54 49.33 21.96 49.24 22.18 49.14 22.39 49.04 22.61 54 55 50.24 22.37 50.15 22.59 50.05 22.81 49.95 23.03 55 56 51.16 22.78 51.06 23.00 50.96 23.22 50.86 23.44 56 57 52.07 23.18 51.97 23.41 51.87 23.64 51.76 23.86 57 58 52.99 23.59 52.88 23.82 52.78 24.05 52.67 24.28 58 59 53.90 24.00 53.79 24.23 53.69 24.47 53.58 34.70 59 60 61 54.81 24.40 54.71 24.64 54.60 24.88 54.49 25.12 60 61 55.73 24.81 55.62 25.05 55.51 25.30 55.40 25.54 62 56.64 25.22 56.53 25.46 56.42 25.71 56.30 25.96 62 63 57.55 25.62 57.44 25.88 57.33 26.13 57.21 26.38 63 64 58.47 26.03 58.35 26.29 58.24 26.54 58.12 26.79 64 65 59.38 26.44 59.26 86.70 59.15 26.96 59.03 27.21 65 66 60.29 26.84 60.18 27.11 60.06 27.37 59.94 27.63 66 67 61.21 27.25 61.09 27.52 60.97 27.78 60.85 28.05 67 68 62.12 27.66 62.00 27.93 61.88 28.20 61.75 28.47 68 69 63.03 28.06 62.91 28.34 62.79 28.61 62.66 28.89 69 70 71 63.95 28.47 63.82 28.75 63.70 29.03 63.57 29.31 29.72 70 71 64.86 28.88 64.74 29.16 64.61 29.44 64.48 72 65.78 29.28 65.65 29.57 65.52 29.86 65.39 30.14 72 78 66.69 29.69 66.56 29.98 66.43 30.27 66.29 30.. 56 73 74 67.60 30.10| 67.47 30.39 67.34 30.69 67.20 30.98 74 75 68.62 30.51 68.38 30.80 68.25 31.10 68.11 31.40 75 76 69.43 30.91 69.29 31.21 69.16 31.52 69.02 31.82 76 77 70.34 31.32 70.21 31.63 70.07 31.93 69.93 32.24 77 78 71.26 31.73 71.12 32.04 70.98 32.35 70.84 32.66 78 79 72.17 32.13 72.03 32.45 71.89 32.76 171.74 33.07 79 80 81 73.08 32.54 72.94 32.86 72.80 33.18 72.65 33.49 80 81 74.00 32.95 73.85 33.27 73.71 33.59 73.56 33.91 82 74.91 33.35 74.76 33.68 74.62 34.00 74,47 34.33 82 83 75.82 33.76 75.68 34.09 75.53 34.42 75.38 34.75 83 84 76.74 34.17 76.59 34.50 76.44 34.83 76.28 35.17 84 85 77.65 34.57 77.50 34.91 77.35 35.25 77.19 35.59 85 86 78.56 34.98 78.41 35.32 78.26 35.66 178.10 36.00 86 87 79.48 35.39 79.32 35.73 79.17 36.08 179.01 36.42 87 88 80.39 35.79 80.24 36.14 80.08 36.49 i 79.92 36.84 88 89 81.31 36.20 81.15 36.55 80.99 36.91 180.82 37.26 89 90 91 82.22 136.61 82.06 36.96 81.90 37.32 37.74 81.73 37.68 90 91 83.13 37.01 82.97 37.38 82.81 82.64 38.10 92 84.05 37.42 83.88 37.79 83.72 38.15 83.55 38.. 52 92 93 84.96 37.83 84.79 38.20 84.63 38.57 84.46 38.94 93 94 85.87 38.23 85.71 38.61 85.54 38.98 85.37 39.35 94 95 86.79 38.64 86.62 39.02 86.45 39.40 86.27 39.77 95 96 87.70 39.05 1 87.53 39.43 87.36 39.81 87.18 40.19 96 97 88.61 39.45 1 88.44 39.84 88.27 40.23 88.09 40.61 97 98 89.53 39.86 1 89.35 40.25 89.18 40.64 89.00 41.03 98 99 90.44 40.27 90.26 40.66 90.09 41.05 89.91 41.45 99 100 .2 Q 91.35 40.67 91.18 41.07 91.00 41.47 90.81 41.87 100 Q Dep. Lat. 1 Dep. Lat. Dep. Lat. Dep. Lat. 66 Deg. 65| Deg. 65h Deg. *65i Deg. rSAVER5E T-JlELE. E 1 25 Deg. 25i Deg. 25h Deg. ' 261 i Deg. ' I i 1 Lat. j Dep. 1 0.42! Lat. Dep. Lat. i Dep. 0.90: 0.43 Lat. 1 Dep. 1 2 i 0.91 i 0.90 0.43 1 0.90. 0.431 1 2 1.81 0.85. 1.81 0.85 i 1.81 0.86; 1.80 0.87! 2 3 2.72 : 1.27 1 2.71 1.28 '■ 2.71! 1.29^ 2.70 1.30' 3 4 3.63 1.69 > 3.62! 1.7n 3.61; 1,72; 3.60; 1.74: 4 5 4.53 2.11! 4.52 1 2.13 1 4.51 1 2.15 4.50: 2.17 [ 5 6 5.44 2.54 j 5.43 2.56 ; 5.42! 2.58 i 5.40 2.61 6 7 6.34 2.96 0.33 i 2.99} 7.24 3.41 6.32 3.01! 6.30 3.04 7 8 7.25 3.-38 7.22 3.44! 7.21! 3.48 j 8 9 8.16 3.30' 8.14 3.84" 8.12: 3.87;! 8.11' 3.91 9 10 9.06: 4.23 9.04 4.27; 9.03 4.31 '' 9.01 9.93 4.74 9.91 4.34 10 11 9.97 4.35 ! 9.95 4.69 ' 4.78 11 12 llO.SSi 5.07 : 10.85 5.12 ! 10.83 5.17 : 10.81 > 5.21 12 13 i 11.78 1 5.49 ' 11.76 5.55; 11.73: 5.60 111.71; 5.65 13 14 12.69 1 5.92 : 12.66 5.97 j 6.40 1 12.64' 6.03 i 12.61 ! 6.08 14 15 13.59 6.34 '■ 13.57 13.54; 6.46 ! 13.51 ■> 6.52 15 16 14.50: 6.76 : 14.47 6.83 ; 14.44' 6.89 1 14.41 : 6.95 16 17 15.41 ; 7.1s i 15.38 7.25 ; 15.34 1 7.32 1 15.31 7.39 17 18 16.31! 7.61 i 16.28 7.68 j 16.25! 7.75 16.21' 7.82 18 19 17.22 i 8.03 : 17.18 8.10 i 17.151 8.18 17.11 8.25 19 20 1 18.13; 8.45 '■ 18.09 8.53 ! 18.05 1 8.61; 18.95 i 9.04 18.01 8.69 20 21 ' 19.03! 8.87 18.99 1 8.96 18.91 9.12 21 22 ,19.94; 9.30 19.90 9.38! 19.86: 9.47 119.82 9.56 22 23 '20.85 1 9.72 20.80 9.81 20.76 i 9.90! 20. 72 9.99 23 24 '21.75 1 10.14(21.71 10.24 21.66 : 10.33 21.62 10.43 24 25 ; 22.66 1 10.57 22.61 1 10.66 22.56 1 10.76 22.52 10.86 25 26 1 23.56'; 10.99 23.52} 11.09 23.47! 11. 19 ij 23.42 11.30 26 27 ! 24.47 11.41:1 24.42 1 11.52 24.37 11.62 S; 24.32 11.73 27 28 25.38 1 11.83!; 25.32 11.94 -25.27! 12.05 1^ 25.22 12.16 OiJ 29 26.28 j 12.26 [i 26.23 12.37 26.17' 12.48 126.12 12.60 29 .30 27.19 1 12.68 i 27.13 12.80, 27.08! 12.92 1127.02 27.98! 13.35 !' 27.92 13.03 30 31 j 2S.i0 • 13.10; 28.04! 13.22 13.47 31 32 29.00 ; 13.52 28.94! 13.65 28.88! 13.78 " 28.82 13.90 ' 32 33 [29.91 ; 13.95 1' 29.85 • 14.0S 29.79 14.21 !' 29.72 14.34 33 34 30.81! 14.37 ii 30.75: 14.50. 30.69 14.64' 30.62 14.77 a4 35 ! 31.72; 14.79/ 31.66 : 14.93 31.59: 15.07 |31..52 15.21 35 36 32.63; 15.21 ,; 32.56 ' 15.36 32.49 1 15.50 j 32.43 15.64 36 37' 33.53' 15.64 : 33.46 j 15.78 33.40, 15.93 33.33 16.07 : 37 .38 34.44 1 16.06 134.37; 16.21 34.30 16.36' 34.23 16.51 38 39 ; 35 . 35 j 16.48 i 35.27 : 16.64 35.20; 16.79 '35.13 16.94 39 40 i 36.25 1 16.90 1 36.18 17.06 36.10 17.22'. 36.03 17.38, 40 41 ! 37.16 17.33 37.08 17.49 37.01 17.65: 36.93 17.81 41 42 i 3S . 06 17.75 37.99 17.92 37 .91 ' 18.08 .37 .83 18.25 42 43 i 38.97 18.17 38.89 18.34; 38.81 | 18.51 ^ 38.73 18.68 43 44- 39. S« 18.60 39.80 18.77 39.71 1 18.94 ;; 39.63 19.12 44 45 40 . 78 19.02 1 40.70 ; 19.20 ^40.62 19.37 .40.53 19.55 4-5 46 141.69 19.44 ' 41.60 19.62 41.52 19.80 41.43 19.98 46 47! 42.60 19.86 1 42.51 20.05 42.42 20.23 42.33 20.42 47 48 143.60 20.29 i 43.41 20.48 43.32 20.66 43.23 20.85 48 49 44.41 20.71 : 44.32 20.90 44.23 21.10 44.13 21.29 49 50 ; 45.32 21.13 1 45.22 21.33 45.13 ; 21.53 ,45.03 21.72 ; 50 1 Dep. Lat. Dep. Lat, Dep. Lat. ij Dep. |L.. i X 65 Deg. 4 641 Deg. 64i Deg. 64i Deg. i X TRAVERSE TABLE. 5S 2 i 9 51 25 Deg. 25i Deg. 25i Deg. 251 Deg. to 1 51 Lat. 46.22 Dep. Lat. 46.13 Dep. Lat. 46.03 Dep. Lat. Dep. 21.55 21.75 21.96 45.94 22.16 52 47.13 21.98 47.03 22.18 46 . 93 22.39 46.84 22.59 52 53 48.03 22.40 47.94 22.61 47.84 22.82 47.74 23.03 53 54 48.94 22.82 48.84 23.03 48.74 23.25 48.64 23.46 54 55 49.85 23.24 49.74 23.46 49.64 23.68 49.54 23.89 55 56 50.75 23.67 50.65 23.89 50.54 24.11 50.44 24.33 56 57 51.66 24.09 51.55 24.31 51.45 24.54 51.34 24.76 57 58 52.57 24.51 52.46 24.74 52.35 24.97 52.24 25.20 58 59 53.47 24.93! 53.36 25.17 53.25 25.40 53.14 25.63 59 60 61 54.38 25.36 j 54.27 55.17 25.59 54.16 25.83 54.04 54.94 26.07 26.50 60 61 55.28 25.78 26.02 55.06 26.26 62 56.19 26.20 56.08 26.45 55.96 26.69 55.84 26.94 62 63 57.10 26.62 .56.98 26.87 56.86 27.12 56 . 74 27.37 63 64 58.00 27.05 57.89 27.30 57.77 27.55 57.64 27.80 64 65 58.91 27.47 58.79 27.73 58.67 27.98 58.55 28.24 65 66 59.82 27.89 59.69 28.15 59.57 28.41 59.45 28.67 66 67 60.72 28.32 1 60.60 28.58 60.47 28.84 60.35 29.11 67 68 61.63 28.74 61.50 29.01 61.. 38 29.27 61.25 29.54 68 69 62.54 29.16 1 62.41 29.58 1 63.31 29.43 62.28 29.71 '62.15 29.98 69 70 71 63.44 29.86 30.29 63.18 30.14! 63.05 30.41 70 71 64.35 30.01 ; 64.22 64.08 30.57 j! 63.95 30.85 72 65.25 30.43 i 65.12 30.71 64.99 31.00 1; 64.85 31.28 72 73 66.16 30.85! 66.03 31.14 65.89 31.43 ' 65.75 31.71 73 74 67.07 31.27 1! 66.93 31.57 66.79 31.86, 66.65 32.15 74 75 67.97 31.70 li 67.83 31.99 67.69 32.29 67.55 32.58 75 76 68.88 32.12!l 68.74 33.42 68.60 32.72 68.45 33.02 76 77 69.79 32.. 54 69.64 32.85 69.50 33.15 69.35 33.45 77 78 70.69 32.96 70.55 33.27 i 70.40 33.58 70.25 33.89 78 79 71.60 33.39 71.45 33.70 171.30 34.01 71.16 34.32 79 80 91 72.. 50 33.81 72.36 73.26 34.13 72.21 34.44 34.87 72 06 34.76 35.19 80 81 73.41 34.23 34.55 73.11 72.96 82 74.32 34.65 74.17 34.98 74.01 35.30 73.86 35.62 82 83 75.22 35.08 75.07 35.41 74.91 .35.73 74.76 36.06 83 84 76.13 35.. 50 75.97 35.83 ; 75.82 36.16 75.66 36.49 84 85 77.04 35.92 76.88 36.26 ' 76.72 .36.59 76.56 36.93 85 86 77.94 36.35 77.78 36.68 77.62 37.02 77.46 37.36 86 87 78.85 36.77 78.69 37.11 78.52 37.45 78.36 37.80 87 88 79.76 37.19 79.59 37.54 79.43 37.88 79.26 38.23 88 89 80.66 37.61 80.50 37.96 ; 80.33 38.32 80.16 38.67 89 90 91 81.57 38.04 81.40 38.39 1 81.23 38.75 81.06 39.10 39.53 90 91 82.47 38.46 82.31 38.82 82.14 39.18 81.96 92 83.38 38.88 83.21 39.24 : 83.04 39.61 82.86 39.97 92 93 84.29 39.30 84.11 39.67; 83.94 40.04 83.76 40.40 93 94 85.19 39.73 85.02 40.10 : 84.84 40.47 84.67 40.84 94, 95 86.10 40.15 85.92 40.52 85.75 40.90 85.57 41.27 93' 96 87.01 40.. 57 86.83 40.95 86.65 41.33 86.47 41.71 96 97 87.91 140.99 87.73 41.38 87.55 41.76 87.37 42.14 97 98 88.82 141.42 88.64 41.80 88.45 42.19 88.27 42.58 98 99 89.72 41.84 89.. 54 42.23 89.36 42.62 89.17 43.01 99 100 V 1 .2 90.63 42.26 90.45 42.66: 90.26 43.05 90.07 43,44 100 i 1 s Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 63 Deg. 641 Deg. 64i Deg. 64^ Der 34 TRAVERSE TABLE. 1 .Oe. 26i Deg. 26^ Deg. 261 Deg. s o c Lat. Dep. Lat. Dep. Lat. I Dep. Lat. Dep. 1 1 0.90 0.44 0.90 0.44 0.89 1 0.45 0.89 0.45 1 1 2 1.80 0.88 1.79 0.88 1.79; 0.89 1.79 0.90 2 1 3 2.70 1.32 2.69 1.33 2.68 1 1.34 2.68 1.35 3 1 4 3.60 1.75 3.59 1.77 3.58! 1.78 3.57 1.80 4 5 4.49 2.19 4.48 2.21 4.47 1 2.23 4.46 2.25 5 6 5.39 2.63 5.38 2.65 5.37 3.88 5.-36 2.70 6 7 1 6.29 3.07 6.28 3.10 6.26 3.12 6.25 3.15 7 8 7.19 3.51 7.17 3.54 7.16 3.57 7.14 3.60 8 9 8,09 3.95 8.07 3.98 8.05! 4.02 8.04 4.05 9 10 8.99 4,38 8.97 4.42 8.95! 4.46 8.93 4.50 10 11 9,89 4.82 9.37 4.87 9.84 4.91 9.82 4.95 1 11 12 10.79 5,26 10.76 5.31 ! 10.74 5.35 10.72 5.40 12 13 11.68 5.70 11.66 5.75 i 11.63 5.80 11.61 5.85 13 14 12.58 6.14 12.. 56 6.19 12.53 6.25, 12.50 6.30 14 15 1 13.48 6. .58 1 13.45 6,63 13.43 6.69 ! 13.39 6.75 15 16 , 14.38 7.01 ! 14.35 7.08 14.32 7.l4ii 14.29 7.20 16 1 17 15.28 7.45! 15.25 7.52' 15.21 7.59 1 15.18 7.65 i 17 1 18 16.18 7.89 1 16.14 7.96 16.11 8.03 j! 16.07 8.10 18 19 17.08 8.331 17.04 8.40 17.00 8.48;! 16.97 8.55 19 20 17.98 8.77: 9,21] 17.94 8.85 17.90 8.92 Ij 17.86 9. CO 20 21 ; 18.87 18.83 19.73 9.29 i 18.79 9.37! 18.75 i 9.45 21 22 1 19,77 9.64 9.73 1 19.69 i 20,58 9.82 ! 19.65 9.90 22 23 20.67 10.08 '20.63 10.17 10.26 '20.54 10.35 23 24 121.57 10.52 121.52 10.61 21.48 10.71 1,21.43 10.80 24 25 i 22.47 10,98 122.42 11.06 22.37 11.15 1,22.32 11.25 25 26 j 23.37 11.40 1! 23.32 11.50 23.27 11.60 1^23.22 11.70 26 27 124.27 11.84 124.22 11.94 24.16 12.05 !i 24.11 12.15 27 28 i 25.17 12.27 : 25.11 12.38 25.06 12.49 1:25.00 12.60 28 29 126.06 : 12.71 26.01 12.83 25.95 12.94 i 25.90 13.05 29 30 126.96 ' 13.15 26.91 27.80 13.27 13.71 26.85 13.39 26.79 13.50 30 31 '27.S6 13. 5 J 27.74 13.83 ji 27.68 13.95 31 32 28.76 14,03 28.70 14.15 28.64 14.28 ;28..58 14.40 32 33 29.66 14.47 129.60 14.60 29.53 14.72 129.47 14.85 33 34 30.56 14.90 30.49 15.04 30.43 15.17 30.36 15.30 34 35 31.46 15.34 31.39 15.48 31.32 15.62 131.25 i 15.75 35 36 32.36 15.78 1 32.29 15.92 32.22 16.06 132.15! 16.20 1 36 | 37 133.26 16.22 33,18 i 16.36 33.11 16.51 133.04; 16.65 1 37 38 134.15 16,66 134.08 16.81 34,01 16.96 33.93 i 17.10 38 39 35.05 17.10 134.93 1 17.25 1 34,90 17.40 1 34.83! 17.55 39 40 135.95 41 ' 36,85 17.53 17.97 ; 35,87 i 17.69 j 35.80 17.85 [35.72: 18.00 ': 36.61 1 18,45 40 41 I 36 , 77 1 18.- 13 1 36.69 18.29 42 1 37.75 18 41 '■ 37.67 ! 18.58 37.. 59 18.74 [I 37.51 i 18.90 42 43 I 38,65 18.85 1 38,57 ; 19.02 38.48 19.19 1,38.40 1 19.35 43 44 39.55 19.29 ! 39.46 19.46 39.38 19.63 39.29 , 19.80 44 ^5 40.45 19,73 40.36 19.90 40.27 20.08 j 40.18 20.25 45 46 t 41 , 34 20.17 41.26 20.35 41.17 20.53 :41.08 20.70 46 47 142,24 20.60 42.15 20.79 42.06 20.97 41.97 ; 21.15 47 48 143.14 21.04 43.05 21.23 42.96 21.42 42.86 21.60 48 49 ' 44.04 21.48 143.95 1 21.67 43.85 21.86 43.76 22.05 49 50 144.94 21.92 , 44.84 22.11 44.75 22.31 J44.65 1 22.50 50 i 1 Dep. Lat. j Dep. Lat. Dep Lat. Dep. ! Lat. .2 .2 64 Deg 631 De^. 63^ Deg. 63i Deg. TRAVERSE TABLE. bb 9. P 51 26 Deg. 26k Deg. 26i Deg. 26| Deg. 5 1 Lat. Dep. Lat. Dep. Lat. 45.64 Dep. 22.76 Lat. 45.54 Dep. 45.84 22.36 45.74 22.56 22.96 ^• 52 46.74 22.80 46.64 23.00 46.54 23.20 46.43 23.41 52 53 47.64 23.23 47.53 23.44 47.43 23.65 47.33 23.86 53 54 48.53 23.67 48.43 23.88 48.33 24.09 48.22 24.31 54 55 49.43 24.11 49.33 24.33 49.22 24.54 49.11 24.76 55 56 50.33 24.55 50.22 24.77 50.12 24.99 50.01 25.21 56 57 51.23 24.99 51.12 25.21 51.01 25.43 50.90 25.66 57 58 52.13 25.43 52.02 25.65 51.91 25.88 51.79 26.11 58 59 53.03 25.86 52.92 26.09 52.80 26.33 52.69 26.56 59 60 61 53.93 26.30 53.81 26.54 53.70 26.77 53.58 27.01 60 61 54.83 26.74 54.71 26.98 54.59 27.22 54.47 27.46 62 55.73 27.18 55.61 27.42 55.49 27.66 55.36 27.91 62 63 56.62 27.62 56.50 27.86 56.38 28.11 56.26 28.. 36 63 64 57.52 28.06 57.40 28.31 57.28 28.56 57.15 28.81 64 65 58.42 28.49 58.30 28.75 58.17 29.00 58.04 29.26 65 66 59.32 28.93 59.19 29.19 59.07 29.45 58.94 29.71 66 67 60.22 29.37 60.09 29.63 59.96 29.90 59.83 30.16 67 68 61.12 29.81 60.99 30.08 60.86 30.34 60.72 30.61 68 69 62.02 30.25 61.88 30.52 61.75 30.79 61.62 31.06 69 70 71 62.92 30.69 62.78 30.96 62.65 31.23 62.51 31.51 70 63.81 31.12 63.68 31.40 63.54 31.68 63.40 31.96 71 72 64.71 31.56 64.57 31.84 64.44 32.13 64.29 32.41 72 73 65.61 32.00 65.47 32.29 65.33 32.57 65.19 32.86 73 74 66.51 32.44 66.37 32.73 66.23 33.02 66.08 33.31 74 75 67.41 32.88 67.27 33.17 67.12 33.46 66.97 33.76 75 76 68.31 33.32 68.16 33.61 68.01 33.91 67.87 34.21 76 77 69.21 33.75 69.06 34.06 68.91 34.36 68.76 34.66 77 78 70.11 34.19 69.96 34.50 69.80 34.80 69.65 35.11 78 79 71.00 34.63 70.85 34.94 70.70 35.25 70.55 35.56 79 80 81 71.90 35.07 71.75 35.38 71.59 35.70 71.44 36.01 80 72,80 35.51 72.65 35.83 72.49 36.14 72.33 36.46 81 82 73.70 35.95 73.54 36.27 73.38 36.59 73.22 36.91 82 83 74.60 36.38 74.44 36.71 74.28 37.03 74.12 37.36 83 84 75.50 36.82 75.34 37.15 75.17 37.48 75.01 37.81 84 85 76.40 37.26 76.23 37.59 76.07 37.93 75.90 38.26 85 86 77.30 37.70 77.13 38.04 76.96 38.37 76.80 38.71 86 87 78.20 38.14 78.03 38.48 77.86 38.82 77.69 39.16 87 88 79.09 38.58 78.92 38.92 78.75 39.27 78.58 39.61 88 89 79.99 39.01 79.82 39.36 79.65 39.71 79.48 40.06 89 90 91 80.89 39.45 80.72 39.81 80.54 40.16 80.37 40.51 90 81.79 39.89 81.62 40.25 81.44 40.60 81.26:40.96 91 92 82.69 140.33 82.51 40.69 82.33 41.05 82.15 41.41 92 93 83.59 140.77 83.41 41.13 83.23 41.50 83.05 41.86 93 94 84.49 1 41.21 84.31 41.58 84.12 41.94 83.94 42.31 94 95 85.39 41.65 85.20 42.02 85.02 42.39 84.83 42.76 95 96 86.28 42.08 86.10 42.46 85.91 42.83 85.73 43.21 96 97 87.18 1 42.52 87.00 42.90 86.81 43.28 86.62 43.66 97 98 88.08 42.96 87.89 43.34 87.70 43.73 87.51 i 44.11 98 99 88.98 43.40 88.79 43.79 88.60 44.17 88.40 144.56 99 100 i S9.88 43.84 89.69 44.23 89.49 44.62 89.30 45.01 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Q 64Deg. 631 Deg. 63| Deg. 63i Deg. 56 TRAVERSE TABLE. c p 27 Deg. m Deg. 1 27^ Deg. 27| Deg. 1 Lat. Dep. 0.45 Lat. Dep. , Lat. Dep. Lat. Dep. 1 0.89 0,89 0.46 0.89 0.46 ! 0.88 0.47 2 1.78 0.91 1.78 0.92 1.77 0.92 1.77 0.93 2 3 2.67 1.36 2.67 1.37 2.66 1.39 2.65 1.40 3 4 1 3.56 1.82 3.56 1.83 3.55 1.85 3.54 1.86 4 5 4.45 2.27 4.45 2.29 4.44 2.31 4.42 2.33 5 6 1 5.35 2.72 5.33 2.75 5.32 2.77 5.31 2.79 6 7 1 6.24 3.18 6.22 3.21 6.21 3.23 6.19 3.26 7 8' 7.13 3.63 7.11 3.66 7.10 3.69 7.08 3.72 8 9 8.02 4.09 8.00 4.12 7.98 4.16 7.96 4.19 9 10 11 8.91 4.54 8.89 9.78 4.58 8.87 4.62 8.85 4.66 10 11 9.80 4.99 5.04 9.76 5.08 9.73 5.12 12 10.69 5.45 10.67 5.49 10.64 5.54 10.62 5.59 12 13 11.58 5.90 11.56 5.95 11.53 6.00 11.50 6.05 13 14 12.47 6.36 12.45 6.41 12.42 6.46 12.39 6.52 14 15 13.37 6.81 13.34 6.87 7.33 13.31 6.93 1 13.27 6.98 15 16 14,26 7.26 14.22 14.19 7.39 i 14.16 7.45 16 17 15.15 7.72 15.11 7.78 15.08 ■ 7.85! 15.04 7.92 17 18 16.04 8.17 16.00 8.24 15.97 8.31 1 15.93 8.38 18 19 16.93 8.63 16.89 8.70 16.85 8.77 16.81 8.85 19 20 21 17.82 IS. 71 9.08 17.78 9.16 17.74 9.23 1 17.70 9.31 20 21 9.53, 18.67 9.62 18.63 9.70 i 18.58 9.78 23 19.60 9.99 19.56 10.07 19.51 10.16' 19.47 10.24 22 23 20,49 10.44 11 20.45 10.53 20.40 10.62! 20.. 35 10.71 23 24 21.38 10.90 'j 21.34 10.99 21,29 11.08 21.24 11.17 24 25 22.28 11.35 !' 22.23 11.45 22.18; 11.54 22.12 11.64 25 26 23.17 11.80 i; 23.11 11.90 23.06 12,01 23.01 12.11 26 27 24.06 12.26 ji 24.00 12.36 ^ 23.95 1 12.47, 23.89 12.-57 27 28 24.95 12.71 1:24.89 12.82 24.84] 12.93 24.78 13.04 28 29 35.84 13.17 '25.78 13.28 25.72! 13.39 25.66 13,50 29 30 31 26 . 73 13.62 ii 26.67 13.74 26.61 1 13.85 27.50 1 14.31 26.55 27.43 13.97 30 31 27.62 14.07 i; 27.56 14.19 14.43 32 28.51 14.53 ii 28.45 14.65' 28.38 14.78 ,28.32 14.00 32 33 29 . 40 14,98 1129.34 15.11 29.27 15.24 i 29.20 15.37 33 34 30.29 15.44 1: 30.23 15.57 30.16 15.70 '30.09 15.83 34 35 31.19 15.89 1 31.12 16.03 31.05 16.16 ; 30.97 16.30 35 36 32.08 16.34 |i 32.00 16.48 31.93 1 16.62 ;31.86 16.76 36 37 .32.97 16.80 i 32.89 16.94 32.82 1 17.08 32.74 17,23 37 38 33.86 17.25 |i 33.78 17.40 33.71 i 17.55 33.63 17,69 38 39 34.75 17.71 1 34.67 17.86 34.59 1 18.01 34.51 18,16 39 40 41 35.64 18.10 ; 35.56 18.31 35.48! 18.47 ; 35.40 18.62 40 41 36.53 18.6] ! 36.45 18.77 36.37 18.93 136.28 19.09 42 37.42 19.07 37.34 19.23 37.25 j 19.39 ■37.17 19.56 42 43 38.31 19.52 38.23 19.69 38.14; 19.86 ! 38.05 20.02 43 44 39.20 19.98 1 39.12 20.15 39.03' 20.32 ■ 38 . 94 20.49 44 45 40.10 20.43 '40.01 20.60 39.92 i 20.78 ,39.82 20.95 45 46 40.99 20.88 '40.89 21.06 40.80 ! 21.24 ; 40.71 21,42 46 47 41.88 21.34 Ii 41.78 21.52 41.69 i 21.70 41.59 21,88 47 48 42 . 77 21.79 ;; 42.67 21.98 142.58 122.16 42.48 22.35 48 49 43.66 22.25 |: 43.56 ! 32.44 43.46 122.63 '44.35 1 23.09 43.36 22.82 49 _50 1 .2 44.55 22.70 ,: 44.45 ; 22.89 : 44.25 23.28 _50 5 Dep. Lat. 1 Dep. j Lat. De^. j Dep. 1 Lat. Dep. 1 Lat. 63 Deg. ! I 621 , 62i Deg. 62i ! Deg. TRAVERSE TABLE. 57 o ? "51 27 Deg. 2U Deg. 27i Deg. 27| Deg. 1 « 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 45.44 23.15 45.34 23.35 45.24 23.55 45.13 23.75 52 46.33 23.61 46.23 23.81 46.12 24.01 46.02 24.21 52 53 47.22 24.06 47.12 24.27 47.01 24.47 46.90 24.68 53 54 48.11 24.52 48.01 24,73 47.90 24.93 47.79 25.14 54 55 49.01 24.97 48.90 25.18 48.79 25.40 48.67 25.61 55 56 49.90 25.42 49.78 25.64 49.67 25.86 49.56 26.07 56 57 50.79 25.88 50.67 26.10 50.56 26.32 ,50.44 26. 5U 57 58 51.68 26.33 51.56 26.56 51.45 26.78 51.33 27.01 58 59 52.57 26.79 52.45 27.01 .52.33 27.24 52.21 27.47 59 60 61 53.46 27.24 53.34 27.47 53.22 27.70 53.10 27.94 60 61 54.35 27.69 54.23 27.93 54.11 28.17 53.98 28.40 62 55.24 28.15 55.12 28.39 54.99 28.63 54.87 28.87 62 63 56.13 28.60 56.01 28.85 55.88 29.09 55.75 29.33 63 64 57.02 29.06 56.90 29.30 56.77 29.55 56.64 29.80 64 65 57.92 29.51 57.79 29.76 57.66 30.01 57.52 30.26 65 66 58.81 29.96 58.68 30.22 58.54 30.48 58.41 30.73 66 67 59.70 30.42 59.56 30.68 59.43 30.94 59.29 31.20 67 68 60.59 30.87 60.45 31.14 60.32 31.40 60.18 31.66 68 69 61.48 31.33 61.34 31.59 61.20 31.86 61.06 32.13 69 70 71 62.37 31.78 62.23 32.05 62.09 32.32 61.95 32.59 70 71 63.26 32.23 63.12 32.51 62.98 32.78 62 .'83 33.06 72 64.15 32.69 64.01 32.97 63.86 33.25 63.72 33.52 72 73 65.04 33.14 64.90 33.42 64.75 33.71 64.60 33.99 73 74 65.93 33.60 65.79 33.88 65.64 34.17 65.49 34.46 74 75 66.83 34.05 66.68 34.34 66.53 34.63 66.37 34.92 75 76 67.72 34.50 67.57 34.80 67.41 35.09 67.26 35.39 76 77 68.61 34.96 68.45 35.26 68.30 35.55 68.14 35.85 77 78 69.50 35.41 69.34 35.71 69.19 36.02 69.03 36.32 78 79 70.39 35.87 70.23 36.17 70.07 36.48 69.91 36.78 79 80 81 71.28 36.32 71.12 36.63 70.96 36.94 70.80 37.25 80 81 72.17 36.77 72.01 37.09 71.85 37.40 71.68 37.71 82 73.06 37.23 72.90 37.55 72.73 37.86 72.57 38.18 82 83 73.95 37.68 73.79 38.00 73.62 38.33 73.45 38.65 83 84 74.84 38.14 74.68 38.46 74.51 38.79 74.34 39.11 84 85 75.74 38.59 75.57 38.92 75.40 39.25 75.22 39.58 85 86 76.63 39.04 76.46 39.38 76.28 39.71 76.11 40.04 86 87 77.. 52 39.50 77.34 39.83 77.17 40.17 76.99 40.51 87 88 78.41 39.95 78.23 40.29 78.06 40.63 77.88 40.97 88 89 79.30 40.41 79.12 40.76 78.94 41.10 78.76 41.44 89 90 91 80.19 40.86 80.01 41.21 79.83 41.56 79.65 41.91 90 91 81.08 41.31 80.90 41.67 80.72 42.02 80.53 42.37 92 81.97 41.77 81.79 42.12 81.60 42.48 81.42 42.84 92 93 82.86 42.22 82.68 42.58 82.49 42.94 82.30 43.30 93 94 83.75 42.68 83.57 43.04 83.38 43.40 83.19 43.77 94 95 84.65 43.13 84.46 43.50 84.27 43.87 84.07 44.23 95 96 85.54 43.58 85.35 43.96 85.15 44.33 84.96 44.70 96 97 86.43 44.04 86.23 44.41 86.04 44.79 85.84 45.16 9T 98 87.32 44.49 87.12 44.87 86.93 45.25 86.73 45.63 98 99 88.21 44.95 88.01 45.33 87.81 45.71 87.61 46.10 99 100 c 5 89.10 45.40 88.90 45.79 88.70 46.17 88.50 46.56 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 63 Deg. 621 Deg. 62i Deg. 624 Deg. 58 TRAVERSE TABLE. p 28 Deg. 284 Deg. il 28^ Deg. 281 Deg. 1 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.88 0.47 0.88 0.47 0.88 0.48 0.88 0.48 2 1.77 0.94 1.76 0.95 1.76 0.95 1.75 0.96 2 3 2.65 1.41 2.64 1.42 2.64 1.43 2.63 1.44 3 4 3.53 1.88 3.52 1.89 3.52 1.91 3.51 1.92 4 6 4.41 2.35 4.40 2.37 4.39 2.39 4.38 2.40 5 6 5.30 2.82 5.29 2.84 5.27 2.86 5.26 2.89 6 7 6.18 3.29 6.17 3.31 6.15 3.34 6.14 3.37 7 8 7.06 3.76 7.05 3.79 1 7.03 3.82 7.01 3.85 8 9 7.95 4.23 7.93 4.26 , 7.91 4.29 7.89 4.33 9 iO 11 8.83 4.69 8.81 4.73 8.79 4.77 8.77 4.81 10 9.71 5.16 9.69 5.21 9.67 5.25 9.64 5.29 11 12 10.60 5.63 10.57 5.68 10.55 5.73 10.52 5.77 12 IB 11.48 6.10 11.45 6.15 11.42 6.20 11.40 6.25 13 14 12.36 6.57 12.33 6.63 12.30 6.68 12.27 6.73 14 15 13.24 7.04 13.21 7.10 13.18 7.16 13.15 7.21 15 16 14.13 7.51 14.09 7.57 14.06 7.63 14.03 7.70 16 17 15.01 7.98 14.98 8.05 14.94 8.11 14.90 8.18 17 18 15.89 8.45 15.86 8.52 15.82 8.59 15.78 8.66 18 19 16.78 8.92 16.74 8.99 16.70 9.07 116.66 9.14 19 20 17.66 9.39 17.62 9.47 17.58 9.54 1 17.53 9.62 20 21 18.54 * 9.86 18.50 9.9'4 18.46 10.02 ■18.41 10.10 21 22 19.42 10.33 10.80 19.38 10.41 19.33 10..50 • 19.29 10.58 22 23 20.31 20.26 10.89 20.21 10.97 20.16 11.06 23 24 21.19 11.27 21.14 11.36 21.09 11.45 ,21.04 11.54 24 25 22.07 11.74 22.02 11.83 21.97 11.93 21.92 12.02 25 26 22.96 12.21 22.90 12.31 22.85 12.41 22.79 12.51 26 27 23.84 12.68 23.78 12.78 23.73 12.88 23.67 12.99 27 28 24.72 13.15 24.66 13.25 24.61 13.36 24.55 13.47 28 29 25.61 13.61 25.55 13.73 25.49 13.84 25.43 13.95 29 30 26.49 14.08 26.43 14.20 26.36 14.31 26.30 14.43 30 31 31 27.37 14.55 27.31 14.67 27.24 14.79 27.18 14.91 32 28.25 15.02 28.19 15.15 28.12 15.27 28.06 15.39 32 33 29.14 15.49 29.07 15.62 29.00 15.75 28.93 15.87 33 34 30.02 15.96 29.95 16.09 29.88 16.22 29.81 16.35 34 35 30.90 16.43 30.83 16.57 30.76 16.70 30.69 16.83 35 36 31.79 16.90 31.71 17.04 31.64 17.18 31.56 17.32 36 37 32.67 17.37 32.59 17.51 32.52 17.65 32.44 17.80 37 38 33.55 17.84 33.47 17.99 33.39 18.13 33.32 18.28 38 39 34.43 18.31 34.35 18.46 34.27 18.61 34.19 18.76 39 40 35.32 18.78 35.24 18.93 35.15 19.09 35.07 19.24 40 41 36.20 19.25 36.12 19.41 36.03 19.56 35.95 19.72 41 42 37.08 19.72 37.00 19.88 36.91 20.04 36.82 20.20 42 43 37.97 20.19 37.88 20.35 .37.79 20.52 37.70 20.68 43 44 38.85 20.66 38.76 20.83 38.67 20.99 38.58 21.16 44 45 39.73 21.13 39.64 21.30 39.55 21.47 39.45 21.64 45 46 40.62 21.60 40.52 21.77 40.43 21.95 40.33 22.13 46 47 41.50 22.07 41.40 22.25 41.30 22.43 41.21 22.61 47 48 42.38 22.53 42.28 22.72 42.18 22.90 42.08 23.09 48 49 43.26 23.00 43.16 23.19 43.06 23.38 42.96 23.57 49 50 44.15 23.47 44.04 23.67 43.94 23.86 43.84 24.05 50 C5 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. s ■ 1 62 Deg. 61| Deg. ai^Deg. 6U T>tg. TRAVERSE TABLE. 69 o P 51 28 Deg. 28i Deg. 28i Deg. 281 Deg. 1 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 45.03 23.94 44.93 24.14 44.82 24.34 44.71 24.63 52 45.91 24.41 45.81 24.61 45.70 24.81 45.59 25.01 52 53 46.80 24.88 46.69 25.09 46.58 25.29 46.47 25.49 53 54 47.68 25.35 47.57 25.56 47.46 25.77 47.34 25.97 54 55 48.56 25.82 48.45 26.03 48.33 26.24 48.22 26.45 55 56 49.45 26.29 49.33 26.51 49.21 26.72 49.10 26.94 56 57 50.33 26.76 50.21 26.98 50.09 27.20 49.97 27.42 57 58 51.21 27.23 51.09 27.45 50.97 27.68 50.85 27.90 58 59 52.09 27.70 51.97 27.93 51.85 28.15 51.73 28.38 59 60 61 52.98 28.17 52.85 28.40 52.73 28.63 52.60 28.86 60 61 53.86 28.64 53.73 28.87 53.61 29.11 53.48 29.34 62 54.74 29.11 54.62 29.35 54.49 29.58 54.36 29.82 62 63 55.63 29.58 55.50 29.82 55.37 30.06 55.23 30.30 63 64 56.51 30.05 56.38 30.29 56.24 30.54 56.11 30.78 64 65 57.39 30.52 57.26 30.77 57.12 31.02 56.99 31.26 65 66 58.27 30.99 58.14 31.24 58.00 31.49 57.86 31.75 66 67 59.16 31.45 59.02 31.71 58.88 31.97 58.74 32.23 67 68 60.04 31.92 59.90 32.19 59.76 32.45 59.62 32.71 68 69 60.92 32.39 60.78 32.66 60.64 33.92 60.49 33.19 69 70 71 61.81 32.86 61.66 33.13 61.52 33.40 61.37 33.67 70 71 62.69 33.33 62.54 33.61 62.40 33.88 62.25 34.15 72 63.57 33.80 63.42 34.08 63.27 34.36 63.12 34.63 72 73 64.46 34.27 64.30 34.55 64.15 34.83 64.00 35.11 73 74 65.34 34.74 65.19 35.03 65.03 35.31 64.88 35.59 74 75 66.22 35.21 66.07 35.50 65.91 35.79 1 65.75 36.07 75 76 67.10 35.68 66.95 35.97 66.79 36.26 166.63 36.56 76 77 67.99 36.15 67.83 36.45 67.67 36.74 67.51 37.04 77 78 68.87 36.62 68.71 36.92 68.. 55 37.22 68.38 37.52 78 79 69.75 37.09 69.59 37.39 69.43 37.70 69.26 38.00 79 80 81 70.64 37.56 70.47 37.87 70.31 38.17 70.14 38.48 80 81 71.52 38.03 71.35 38.34 71.18 38.65 71.01 38.96 82 72.40 38.50 72.23 38.81 72.06 39.13 171.89 39.44 82 83 73.28 38.97 73.11 39.29 72.94 39.60 72.77 39.92 83 84 74.17 39.44 73.99 39.76 73.82 40.08 73.64 40.40 84 85 75.05 39.91 74.88 40.23 74.70 40.56 74.52 40.88 85 86 75.93 40.37 75.76 40.71 75.58 41.04 75.40 41.36 86 87 76.82 40.84 76.64 41.18 76.46 41.51 76.28 41.85 87 88 77.70 41.31 77.52 41.65 77.34 41.99 77.15 42.33 88 89 78.58 41.78 78.40 42.13 78.21 42,47 78.03 42.81 89 90 91 79.47 42.25 79.28 42.60 79.09 42.94 78.91 43.29 90 91 80.35 42.72 80.16 43.07 79.97 43.42 79.78 43.77 92 81.23 43.19 81.04 43.55 80.85 43.90 80.66 44.25 92 93 82.11 43.66 81.92 44.02 81.73 44.38 81.54 44.73 93 94 83.00 44.13 82.80 44.49 82.61 44.85 82.41 45.21 94 95 83.88 44.60 83.68 44.97 83.49 45.33 83.29 45.69 95 96 84.76 45.07 84.57 45.44 84.37 45.81 84.17 46.17 96 97 85.65 45.54 85.45 45.91 85.25 46.28 85.04 46.66 97 98 86.53 46.01 86.33 46.39 86.12 46.76 85.92 47.14 98 99 87.41 46.48 87.21 46.86 87.00 47.24 86.80 47.62 99 100 88.29 46.95 88.09 47.33 87.88 47.72 87.67 48.10 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 62 Deg. 611 Deg. 61i Deg. 6U Deg. 60 TRAVERSE TABLE. o s CO 29 Deg. 1 m Deg. . . . . . !i 29 i Deg. 291 Deg. 1 Lat. Dep. Lat. Dep. Lat. 1 Dep. Lat. Dep. 0.87 0.48 0.87 0.49 0.87 1 0.49 1 0.87 0.50 1 2 1.75 0.97 1.74 0.98 1.74 0.98 1.74 0.99 2 3 2.62 1.45 2.62 1.47 2.61 1.48 2.60 1.49 3 4 3.50 1.94 3.49 1.95 3.48 1.97 3.47 i 1.98 4 5 4.37 2.42 4.36 2.44 4.35 2.46 4.34 2.48 5 6 5.25 2.91 5.23 2.93 5.22 2.95 5.21 2.98 6 7 6.12 3.39 6.11 3.42 6.09 3.45 6.08 3.47 7 8 7.00 3.88 6.98 3.91 6.96 3.94 6.95 3.97 8 9 7.87 4.36 7.85 4.40 7.83 4.43 7.81 4.47 9 10 11 8.75 9.62 4.85 8.72 4.89 8.70 4.92 1 5.42 1 8.68 4.96 10 11 5.33 9.60 5.37 9.57! 9.55 5.46 12 10.50 5.82 1 10.47 5.86 10.44 5.91 1 10.42 5.95 12 13 11.37 6.301 11.34 6.35 11.31 6.40 i 11.29 6.45 13 14 12.24 6.791 12.21 6.84 12.18 6.89 ! 12.15 6.95 14 15 13.12 7.27 1 13.09 7.33 13.06 7.39 ; 13.02 7.44 15 16 13.99 7.76 13.96 7.82 13.93 7.88 13.89 7.94 16 17 14.87 8.24 14.83 8.31 14.80 8.37 j 14.76 8.44 17 18 15.74 8.73 15.70 8.80 15.67 8.86 15.63 8.93 18 19 16.62 9.21 1 16.58 9.28 16.54 9.36^ 16.50 9.43 19 20 21 17.49 9.701 17.45 9.77 17.41 9.85 1 17.36 9.92 20 18.37 10.181 18.32 10.26 1*8.28 10.34 1 18.23 10.42 21 22 19.24 10.671 19.19 10.75 19.15 10.83 i 19.10 10.92 22 28 20.12 11.15' 20.07 11.24 20.02 11.33 1 19.97 11.41 23 24 20.99 11.64 20.94 11.73 20.89 11.82 !l 20.84 11.91 24 25 21.87 12.12 21.81 12.22 21.76 12.31 ii 21.70 12.41 25 26 22.74 12.60 22.68 12.70 22.63 12.80 !i 22.57 12.90 26 27 23.61 13.09 23.56 13.19 23.50 13.30 i 23.44 13.40 27 28 24.49 13.57 24.43 13.68 24.37 13.79 24.31 13.89 28 29 25.36 14.06 25.30 14.17 25.24 14.28 25.18 14.39 29 30 31 26.24 14.54 26.17 14.66 26.11 14.77 26.05 14.89 30 27.11 15.03 27.05 15.15 26.98 15.27 ,26.91 15.38 81 32 27.99 15.51 27.92 15.64 27.85 15.76 27.78 15.88 82 38 28.86 16.00 28.79 16.12 28.72 16.25 28.65 16.38 88 34 29.74 16.48 29.66 16.61 29.59 16.74 29.52 16.87 34 85 30.61 16.97 30.54 17.10 30.46 17.23 30.39 17,37 35 86 31.49 17.45 31.41 17.59 31.33 17.73 31.26 17.86 36 37 32.. 36 17.94 32.28 18.08 132.20 18.22 32.12 18.36 37 8S 33.24 18.42 33.15 18.57 33.07 18.71 32.99 18.86 88 89 34.11 18.91 34.03 19.06 33.94 19.20 33.86 19.35 89 40 34.98 19.39 34.90 19.. 54 34.81 19.70 34.73 19.85 40 41 41 35.86 19.88 35.77 20.03 35.68 20.19 35.60 20.34 42 36.73 20.36 36.64 20.52 36.55 20.68 36.46 20.84 42 48 37.61 20.85 37.52 21.01 37.43 21.17 37.33 21.34 43 44 38.48 21.33 38.39 21.. 50 38.30 21.67 38.20 21.83 44 45 39.36 21.82 39.26 21.99 39.17 22.16 39.07 22.33 45 46 40.23 22.30 40.13 22.48 40.04 22.65 39.94 22.83 46 47 41.11 22.79 41.01 22.97 40.91 23.14 40.81 23.32 47 48 41.98 23.27 41.88 23.45 41.78 23.63 41.67 23.82 48 49 42.86 23.76 42.75 23.94 42.65 24.13 42.54 24.31 49 50 43.73 24.24 43.62 24.43 43.52 24.62 43.41 24.81 50 a S .2 O Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 .2 Q 61 Deg. 60f Deg. 60i Deg. 60i Deg. TRAVERSE TABLE. 6i 1 o p ~51 29 Deg. 29i Deg. 29^ Deg. 29| Deg. 1 "51 Lat, Dep. Lat. Dep. Lat. Dep. Lat. Dep. 44.61 24.73 44.50 24.92 44.39 25.11 44.28 25.31 52 45.48 25.21 45,37 25.41 45.26 25.61 45.15 25.80 52 53 46.35 25.69 46.24 25.90 46.13 26.10 46.01 26.30 53 54 47.23 26.18 1 47.11 26.39 47.00 26.59 46.88 26.80 54 55 48.10 26.66 1 47.99 26.87 47.87 27.08 47.75 27.29 55 56 48.98 27.15 48.86 27,36 48.74 27.58 48.62 27.79 56 57 49.85 27.63 49.73 27.85 49.61 28.07 49.49 28.28 bV 58 50.73 28.12 50.60 28.34 50.48 28.56 50.36 28.78 58 59 51.60 28.60 51.48 28.83 51.35 29.05 51.22 29.28 by 60 '61 52.48 29.09 29.57 52.35 29.32 52.22 29.55 52.09 29,77 60 61 53.35 53.5i2 29.81 53.09 30.04 52.96 30,27 62 54.23 30.06 54.09 30.29 53.96 30.53 53.83 30.77 62 63 55.10 .30.54 54.97 30.78 .54.83 31.02 54.70 31.26 63 64 55.98 131.03 1 55.84 31.27 55.70 31.52 55.56 31.76 64 65 56.85 31.51 56.71 31.76 56.57 32.01 56.43 32.25 6b 66 57.72 32.00 57.58 32.25 57.44 32.50 .57.30 32.75 66 67 58.60 32.48 .58.46 32.74 58.31 32.99 58.17 33.25 6V 68 59.47 32.97 .59.33 33.23 59.18 33.48 59.04 33.74 68 69 60.35 33.45 60,20 .33.71 60.05 33.98 59.91- 34.24 69 70 71 61.22 33.94 61.07 34.20 60.92 34.47 60.77 34.74 VO 62.10 34.42 61.95 34.69 61.80 34.96 61.64 35,23 71 72 62.97 34.91 62.82 35.18 62.67 35.45 62.51 35.73 72 73 63.85 35.39 63.69 35.67 63.54 35.95 63.38 36.22 73 74 64.72 35.88 64.56 36.16 64.41 36.44 64.25 36.72 74 75 65.60 36.36 65.44 36.65 65.28 36.93 65.11 37.22 75 76 66.47 36.85 66.31 37.14 66.15 37,42 65.98 37.71 76 77 67.35 37.33 67.18 37.62 67.02 37.92 66.85 38.21 77 78 68.22 37.82 68.05 38.11 67.89 38.41 67.72 38.70 78 79 69.09 38.30 68.93 38.60 68.76 38.90 68.59 39.20 79 80 81 69.97 70.84 38.78 69.80 39.09 69.63 39.39 69.46 39.70 80 81 39.27 70.67 39.58 70., 50 39.89 70.. 32 40.19 82 71.72 39 . 75 71.54 40.07 71.37 40.38 71 . 19 40.69 82 83 72.59 40.24 72.42 40.56 72.24 40.87 72.06 41 . 19 83 84 73.47 40.72 73.29 41.04 73.11 41.36 72.93 41.68 84 85 74.34 41.21 74.16 41.53 73.98 41.86 73.80 42.18 85 86 75.22 41.69 75.03 42.02 74.85 42.35 74.67 i 43.67 86 87 76.09 42.18 75.91 42.51 75.72 42.84 75.53 43.17 87 88 76.97 42.66 76.78 43.00 76.59 43.33 76.40 43.67 88 89 77.84 43.15 77.65 43.49 77.46 43.83 77.27 44.16 89 90 91 78.72 43.63 78.52 43.98 78.33 44.32 44.81 78.14 44.66 90 79.59 44.12 79.40 44.46 79.20 79.01 45.16 91 92 80.46 44.60 80.27 44.95 80.07 45.30 79.87 45.65 92 93 81.34 45,09 81.14 45.44 80.94 45.80 80.74 46.15 93 94 82.21 45.57 82.01 45.93 81.81 46.29 81.61 40.64 94 95 83.09 46.06 82.89 46.42 82.68 46.78 82.48 47.14 95 96 83.96 46.54 83.76 46.91 83.55 47.27 83.35 47.64 96 97 84.84 47.03 84.63 47.40 84.42 47.77 84.22 48.13 97 98 85.71 1 47.51 85.50 47.88 85.29 48.26 85.08 48.63 98 99 86.59 '48.00 86.38 48.37 86.17 48.75 85.95 49.13 99 100 i 5 87.46 i 48.48 87.25 48.86 87.04 49.24 86.82 49.62 100 1 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 61 Deg. 601 Deg. 601 Deg. 60i Deg. 62 TKAVERSE TABLE, 1 30 Deg. 304 Deg. 30f Deg. 301 Deg. 3 o a "1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.87 0.50 0.86 0.50 0.86 0.51 0.86 0.51 2 1.73 1.00 1 1.73 1.01 1.72 1.02 1.72 1.02 2 3 2.60 1.50 2.59 1.51 2.58 1.52 2.58 1.53 3 4 3.46 i 2.00 3.46 2.02 3.45 2.03 3.44 2.05 4 5 4.33 2.50 4.32 2.52 4.31 2.54 4.30 2.56 5 6 5.20 3.00 5.18 3.02 5.17 3.05 5.16 3.071 6 7 6.06 3.50 6.05 3.53 6.03 3.55 6.02 3.58 7 8 6.93 4.00 6.91 4.03 6.89 4.06 6.88 4.09 8 9 7.79 4.50 7.77 4.53 7.75 4.57 7.73 4.60 9 10 11 8.66 5.00 8.64 5.04 8.62 5.08 8.59 5.11 10 11 9.53 5.50 9.50 5.54 9.48 6.58 9.45 5.62 12 10.39 6.00 10.37 6.05 10.34 6.09 10.31 6.14 12 13 11.26 6.50 11.23 6.55 11.20 6.60 11.17 6.65 13 14 12,12 7.00 12.09 7.05 12.06 7.11 12.03 7.16 14 15 12.99 7.50 12.96 7.56 12.92 7.61 12.89 7.67 15 16 13.86 8.00 13.82 8.06 13.79 8.12 13.75 8.18 16 17 14.72 8.50 14.69 8.56 14.65 8.63 14.61 8.69 17 18 15.59 9.00 15.55 9.07 15.51 9.14 15.47 9.20 18 19 16.45 9.50 16.41 9.57 16.37 9.64 16.33 9.71 19 20 21 17.32 10.00 17.28 10.08 1 17.23 10.15 17.19 10.23 20 21 18.19 10.50 1 18.14 10.58: 18.09 10.66 18.05 10.74 22 19.05 11.00 19.00 11.08 ; 18.96 11.17 18.91 11.25 22 23 19.92 11.50 19.87 11.59 1 19.82 11.67 19.77 11.76 23 ■24 20.78 12.00 20.73 12.09 ! 20.68 12.18 20.63 12.27 24 25 21.65 12.50 21.60 12.59 1 21.54 12.69 21.49 12.78 25 26 22.52 13.00 22.46 13.10 i 22.40 13.20 22.34 13.29 26 27 23.38 13.50 23.32 13.60 23.26 13.70 23.20 13.80 27 28 24.25 14.00 24.19 14.11 24.13 14.21 24.06 14.32 28 29 25.11 14.50 25.05 14.61 24.99 14.72 24.92 14.83 29 30 31 25.98 15.00 25.92 15.11 25.85 15.23 25.78 15.34 30 31 26.85 15.50 26.78 15.62 26.71 15.73 26.64 15.85 32 27.71 16.00 27.64 16.12 27.57 16.24 27.50 16.36 32 33 28.58 16.50 28.51 16.62 28.43 16.75 28.36 16.87 33 34 29.44 17.00 29.37 17.13 29.30 17.26 29.22 17.38 34 35 30.31 17.50 30.23 17.63 30.16 17.76 30.08 17.90 35 36 31.18 18.00 31.10 18.14 31.02 18.27 30.94 18.41 36 37 32.04 18.50 31.96 18.64 31.88 18.78 31.80 18.92 37 38 32.91 19.00 32.83 19.14 32.74 19.29 32.66 19.43 38 39 33.77 19.50 33.69 19.65 33.60 19.79 33.52 19.94 39 40 41 34.64 20.00 34.55 20.15 34.47 20.30 34.38 20.45 40 41 35.51 20.50 35.42 20.65 35.33 20.81 35.24 20.96 42 36.37 21.00 36.28 21.16 36.19 21.32 36.10 21.47 42 43 37.24 21.50 37.14 21.66 37.05 21.82 36.95 21.99 43 44 38.11 22.00 38.01 22.17 37.91 22.33 37,81 22.50 44 45 38.97 22.50 38.87 22.67 38.77 22.84 38.67 23.01 45 46 39.84 23.00 39.74 23.17 39.63 23.35 39.53 23.52 46 47 40.70 23.50 40.60 23.68 40.50 23.85 40.39 24.03 47 48 41.57 24.00 41,46 24.18 41.36 24.36 41.25 24.54 48 49 42.44 24.50 42.33 24.68 42.22 24.87 42.11 25.05 49 50 o 43.30 25.00 43.19 25.19 43.08 25.38 42.97 25.56 60 s 1 3 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 60 Deg. 591 Deg. 591 Deg. S9i Deg. TRAVERSE TABLE. 63 o ~51 30 Deg. 30i Deg. 30i Deg. 30 Deg. Q O "51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 44.17 25.50 44.06 25.69 43.94 25.88 43.83 26.08 52 45.03 26.00 44.92 2O.20 44.80 26.39 44.69 26.59 52 53 45.90 26.50 45.78 26 70 45.67 26.90 45.55 27.10 53 54 46.77 27.00 46.65 27.20 46.53 27.41 46.41 27.61 54 55 47.63 27.50 47.51 27.71 47.39 27.91 47.27 28.12 55 56 48.50 28.00 48.37 28.21 48.25 28.42 48.13 28.63 56 57 49.36 28.50 49.24 28.72 49.11 2S.93 48.99 29.14 57 58 50.23 29.00 50.10 29.22 49.97 29. i4 49.85 29.65 58 59 51.10 29.50 50.97 29.72 50.84 29.94, 50.70 30.17 1 59 60 61 51.96 30,00 51.83 30.23 30.73 51.70 30.45 51.56 52.42 30.68 1 60 31.19 ! 61 52.83 30.50 52.69 52.56 30.96 62 53.69 31.00 53.56 31.23 53.42 3i.47 53.28 31.70 62 63 54.56 31.50 54.42 31.74 54.28 31.97 1154.14 82.21 63 64 55.43 32.00 55.29 .32.24 55.14 32.48 1 55.00 32.72 04 65 56.29 32.50 56.15 32.75 56.01 32.99!! 55.86 33.23 65 66 57.16 33.00 57.01 33.25 56.87 33.50 1! .56.72 33.75 66 67 58.02 33.50 57.88 33.75 57.73 34.01 1157.58 34.26 67 68 58.89 34.00 58.74 34.26 58.59 34.51 ; .58.44 34.77 68 69 59.76 34.50 59.60 .34.76 59.45 35.02 59.30 35.28 69 70 71 60.62 35.00 1 60.47 35.26 60.31 35.53 60.16 35.79 70 71 61.49 35.50 1 61.33 35.77 61.18 36.04 61.02 36.30 72 62.35 36.00 ' 62.20 36.27 62.04 36.54 61.88 36.81 72 73 63.22 36.50] 63.06 36.78 62.90 37.05 62.74 37.32 73 74 64.09 37.00 63.92 37.28 63.76 37.56 ,63.60 37. S4 74 75 64.95 37.50 64.79 37.78 64.62 38.07 164.46 38.35 75 76 65.82 .38.00' 65.65 38.29 65.48 38.57 65.31 38.86 76 77 66.68 38.50 66.52 38.79 66.35 39.08 66.17 39.37 77 78 67.55 39.00 67.38 39.29 67.21 39.59 67.03 39.88 78 79 68.42 39.50 68.24 39.80 68.07 40.10 67.89 40.39 79 80 81 69.28 40.00 69.11 69.97 40.30 68.93 40.60 68.75 40.90 80 81 70.15 40.50 40.81 69.79 41.11 69.61 41.41 82 71.01 41.00 .70.83 41.31 70.65 41.62 70.47 41.93 82 S3 71.88 4i..50 71.70 41.81 71., 52 42.13 71.33 42.44 83 84 72.75 42.00 72.56 42.32 72.38 42.63 72.19 42.95 84 85 73.61 42.50 1 73.43 42.82 73.24 43.14 73.05 43.46 Sf. 86 74.48 43.00 1 74.29 43.-32 74.10 43.65 73.91 43.97 8f^. 87 75.34 43.50 75.15 43. S3 174.96 44.16 74.77 44.48 87 88 76.21 44.00 I 76.02 44.33 75.82 44.66 75.63 44.99 8H 89 77.08 44.50 ! 76.88 44.84 76.68 45. i7 76.49 45.51 89 90 91 77.94 45.00 77.75 45.. 34 77.55 45.68 77.35 46.02 90 91 78.81 45.50 78.61 45.84 78.41 46.19 178.21 46.53 92 79.67 46.00 79.47 46.35 79.27 46.69 ii 79.07 47.04 92 93 80.54 46.50 80.34 46.85 80.13 47.20 179.92 47 ..55 93 94 81.41 47.00 81.20 47.35 80.99 147.71 180.78 48.06 94 95 82.27 47.50 82.06 47.86 81.85 148.22 81.64 48.57 9r^ 96 83.14 48.00 82.93 48.36 82.72 1 48.72 ; 82.50 49.08 96 97 84.00 48.50 83.79 48.87 83.58 49.23;, 83.36 49.60 97 98 84.87 49.00 84.66 49.37 84.44 49.74 84.22 50.11 98 99 85.74 49.50 85.52 49.87 85.30 50.25 85.08 50.62 99 100 o 1 86.60 50.00 86.38 .50.38 86.16 50.75 85.94 51.13 100 Dep. Lat. Dep Lat. Dep. Lat. Dep. Lat. 60 Deg. 59i Deg. 59i Deg. 59^ Deg. 64 TRAVERSE TABLE. o 5' PS 31 Deg. m Deg. 1 21h Deg. 1 3l| Deg. 1 3 P 1 Lai. 0.86 Dep. Lat. Dep. Lat. 1 Dep. Lat. Dep. 0.51 0.85 0.52 f 0.85 i 0.52 0.85 0.53 1 2 1.71 1.03 1.71 1.0^ 1.71 : 1.04 1.70 1.05 2 3 2.57 1.55 2.56 1.66 2.56 i 1.57 2.55 1.58 3 4 3.43 2.06 1 3.42 2.08 3.41 2.09 3.40 2.10 4 5 4.29 2.58 1 4.27 2.59 4.26 2.61 4.25 2.63 5 6 5.14 3.09 5.13 3.11 5.12 1 3.13 5.10 3.16 6 7 6.00 3.61 5.98 3.63 5.97 1 3.66 5.95 3.68 7 8 6.86 4.12 6.84 4.15 6.82 ; 4.18 6.80 4.21 8 9 7.71 4.64 7.69 4.67 7.67 : 4.70, 7.65 4.74 9 10 11 8.57 9.43 5.15 8.55 5.19 8.53 ■ 5.22 8.50 5.26 10 3.67 9.40 5.71 9.38 ; 5.75! 9.35 5.79 11 12 10.29 6.18 10.26 6.23 10.23 : 6.27j 10.20 6.31 12 13 11.14 6.70 11.11 6.74 11.08 6.79! 11.05 6.84 13 14 12.00 7.21 11.97 7.26 11.94 i 7.31 11.90 7.37 14 15 12.86 7.73 12.82 7.73 12.79 i 7. Ml 12.76 7.89 15 16 13.71 8.24 13.68 8.30 13.64 8.36 i 13.61 8.42 i 16 17 14.57 8.76 14.53 8.82 14.49 8.631 14.46 8.95 17 18 15.43 9.27 15.39 9.34 15.35 9.40 15.31 9.47 18 19 16.29 9.79 16.24 9.86 16.20 , -9.93! 16.16 10.00 19 20 21 17.14 10.30 17.10 10.38 17.05 10.45! 17.01 10.52 20 18.00 10.82 1 17.95 10.89 17.91 10.97 17.86 11.05 21 22 18,86 11.331 18.81 11.41 18.76 11.49 ;i 18.71 11.58 22 23 19.71 11.85 19.66 11.93 19.61 12.02 1 19.56 12.10 23 24 120.57 12.36 20.52 12.45 20.46 12.54 '20.41 12.63 24 25 21.43 12.88 21.37 12.97 21.32 13.06 ! 21.26 13.16 25 26 1 22.29 13.39 22.23 13.49; 22.17 13.58 ! 22.11 13.68 26 27 23.14 13.91 23.03 14.01 1 23.02 14.11 ! 22.96 14.31 27 28 24.00 14.42 23.94 14.53' 23.87 14.63 123.81 14.73 23 29 24.86 14.94 24.79 15.04 24.73 15.15 1 24.66 15.26 29 30 25.71 15.45 25.65 26.50 15.56 16.08. 25.58 15.67 1 25.51 26.36 15.79 3) 31 26.57 15.97 i 26.43 16.20 i 16.31 31 33 27.43 16.48 j 17.00 27.36 18.60 1 27.28 16.72 1 27.21 16.84 32 33 28.29 28.21 17.12; 28.14 17.24 28.06 17.37 33 34 29.14 17.51 29.07 17.64; 28.99 17.76 28.91 17.39 34 35 30.00 18.03 29.93 18.16 29.84 18.29 29.76 18.42 35 36 30.86 18.54 1 30.78 18.68 i 30.70 18.81 30.61. 18.94 36 37 31.72 19.06! 31.63 19.19! 31.55 19.33 31.46 19.47 37 38 32.57 19.57 1 32.49 19.711 32.40 19.85 32.31 20.00 38 39 33.43 20.09 i 33.34 20.23 1 33.25 20.38" 33.16 20.52 39 40 34.29 20.60! .34.20 35.05 20.75* 21.27; 34.11 34.96 20.90 21.42 i 34.01 21.05 40 41 35.14 21.12; 34.86 21.57 41 42 36.00 21.63 35.91 21.79 35.81 21.94 i; 35.71 1 22.10 42 43 36.86 22.15, 36.76 22.31 36.66 22.47!, 36.57 j 22.63 43 U 137.72 22.66! 37.62 22.83 37.52 22.99 |i 37.42 : 23.15 44 45 38.57 23.18 38.47 23.34: 38.37 23.51 || .38.27: 23.68 4.'-. 46 39.43 23.69 39.33 23.88; 39.22 24.03 39.12 1 24.21 46 47 40.29 24.21 40.18 24.38: 40.07 24. 56 !J .39. 97 24.73 47 48 41.14 24.72 41-04 24.90, 40.93 25.08 ;. 40.82 25.26 48 49 42.00 25.24 41.89 25.42; 41.78 25.60 ;!41.67 25.78 49 ii 42.86 25.75 42.75 25.94i 42.63 26.12 j 42.52 | 26.31 50 6 o 5 5 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. i 59 I >eg 581 ] Deg. 58^ Deg. 5Hk 1 leg, "i ^^ - 1 TRAVERSE TABLE. 66 31 Deg. 3U Deg. 3li Deg. 3i| Deg. D w i 1 51 Lat. Dep. Lat. Dep. Lat Dep. Lat. Dep. 43.72 26.27 43.60 26.46 43.48 26.65 43.37 26.84 52 44.57 26.78 44.46 26.98 44.34 27.17 44.22 27.36 52 53 45.43 27.30 45.31 27.49 45.19 27.69 45.07 27.89 53 54 46.29 27.81 46.17 28.01 46.04 28.21 45.92 28.42 54 55 47.14 28.33 47.02 28.53 46.90 28.74 46.77 28.94 55 56 48.00 28.84 47.88 29.05 47.75 29.26 47.62 29.47 56 57 48.86 29.36 48.73 29.57 48.60 29.78 48.47 29.99 57 58 49.72 29.87 49.58 30.09 49.45 30.30 49.32 30.52 58 59 50.57 30.39 50.44 30.61 50.31 30.83 .50.17 31.05 59 60 61 51.43 30.90 1 51.29 31.13 51.16 52.01 31.35 31.87 1 51.02 31.57 60 6i 52.29 3J .42' 52.15 31.65 1 51.87 32.10 62 53.14; 31.93 1 53.00 132.16! 52.86 32.39 52.72 32.63 62 63 54.00 132.45 1 53.86 32.68! 53.72 .32 . 92 53.57 33.15 63 64 54.86 I 32. 96 54.71 33.20! 54.57 33.44 54.42 33.68 64 65 55.72 133.48 55.57 33.72 1 55.42 33.96 55.27 34.20 65 66 56.57 1 33.99 1 56.42 .34.24 156.27 34.48 1 56.12 34.73 66 67 57.43 1 34.51 \ 57.28 34.76 ; 57. 13 35.01 1 56.98 35.26 67 68 58.29 i 35.02! .58.13 35.28 1157.98 35.53 1 57.82 35.78 68 69 59. 14 135.54; 58.99 35.80 11 58.83 36.05 58.67 36.31 69 70 71 60.00 36.05; 59.84 1 36. 3i j 60.70 36,93 59.68 36.57 1 .59.52 60.37 36.83 70 71 60.86 36.57 60.54 37.10 1 37.36 72 61.72 37.08 61.55 137.35 61. ,39 37.62! 61.23 37.89 72 73 62.57 37.60 !i 62.41 37.87 62.24 38.14 62.08 38.41 73 74 63.43 38.11 63.26 138.39 63.10 38.66 62.93 38.94 74 75 64.29 38.63 64.12 138.91 63.95 39.19 63.78 39.47 75 76 65.14 39.14 64.97 139.43 64.80 39.71 64.63 39.99 76 77 66.00 39.66 65.83 ; 39.95 ,65.65 40.23 65.48 40.52 77 78 66.86 40.17 1 66.68 40.46 66.51 40.75 I 66.33 41.04 78 79 67.72 40.69 67.54 40.98 67.36 41.28 167.18 41.57 79 80 81 68.. 57 41.20 69.43 41.72 68 . 39 41.50 68.21 41.80 ; 38.03 1 68.88 42.10 80 8i 69.25 42.02 69.06 42.32 43.62 82 70.29 '42.23 70.10 42.54 69.92 42.84 69 . 73 43.15 8-^ 83 71.14; 42.75' 70.96 43.06 70.77 43.37 1 70.58 43.68 83 84 72.00 1 43.26 71.81 43.58 71.62 43.89 i 71.43 44.20 84 85 72.86] 43.78 72.67 44.10 72.47 44.41 1 72.28 44.73 85 86 73.72 : 44.29 73 . 52 44.61 73.33 44.93 73.13 45.25 88 87 74.57^44.81 74.38 45.13 74.18 45.46 73.9^ 45.78 87 88 75.43 45.32 75.23 45.65 75.03 45 . 98 74.83 46.31 88 89 76.29 '45.84 76.09 46.17 75.88 46.50 1 75.68 46.83 89 90 77.15 46. .35 76.94 46.69 76.74 47.02 1 76.53 77.38 47.36 90 91 78.00 1*46.87 77.80 47.21 77.59 47.55 47.89 91 92 78.86 147.38 78.65 47.73 78.44 48.07!! 78.23 48.41 92 93 79.72 147.90 79.51 48.25 79.30 48.59 79.08 48.94 93 94 80..57: 48.41 80.36 48.76 80.15 49.11 79.93 49.47 94 95 81.43 ,48.93 81.22 49.28 81.00 49.64 80.78 49.99 95 96 82.29 ; 49.44 82.07 49.80 81.85 50.16 81.63 50.52 96 97 83.15 49.96 82.93 50.32 82.71 .50.68 82.48 51.04 97 98 84.00 ; 50.47 83.78 50.84 83.56 51.20 83.33 51.57 9R 99 84.86 50.99 84.64 51.36 84.41 51.73 : 84.18 52.10 99 100 i 2 85.72 Dep. ■51.50 ! Lat. 85.49 51.88 85.26 5i;.25 85.04 .52.62 100 i J (5 Dep. Lat. Dep. Lat. Dep. Lat. 39 Deg. 581 Deg. 581 Deg. 581 Deg. 66 TRAVERSE TABLE. 32 Deg. 32i Deg. 32^ Deg, 1 321 Deg. a Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 1 0.85 0.53 0.85 0.53 0.84 0.54 0.84 0.54 1 2 1.70 1.06 1.69 1.07 1.69 1.07 1.68 1.08 2 3 2.54 1.59 2.54 1.60 2.53 1.61 2.52 1.62 3 4 3.39 2.12 3.38 2.13 3.37 2.15 3.36 2.16 4 5 4.24 2.65 4.23 2.67 4.22 2.69 4.21 2.70 5 6 5.09 3.18 5.07 3.20 5.06 3.22 5.05 3.25 6 7 5.94 3.71 5.92 3.74 5.90 3.76 5.89 3.79 7 8 6.78 4.24 6.77 4.27 6.75 4.30 6.73 4.33 8 9 7.63 4.77 7.61 4.80 7.59 4.84 7.57 4.87 9f 10 11 8.48 5.30 8.46 5.34 8.43 5.37 8.41 5.41 10 11 9.33 5,83 9.30 5.87 9.28 5.91 ii 9.25 5.95 12 10.18 6.36 10.i5i 6.40 10.12 6.45 ll 10.09 6.49 12 13 11.02 6.89 1 10.99 6.94 10.96 6.98 10.93 11.77 7.03 13 14 11.87 7.42 1 11.84 7.47 11.81 7.62 7.57 14 15 12.72 7.95 1 12.69 8.00 12.65 8.06 ; 12.62 8.11 15 16 13.57 8.48 1 13.53 8.54 13.49 8.60 i 13.46 8.66 16 17 14.42 9.01 1 14.38 9.07 14.34 9.13 i 14.30 9.20 17 18 15.26 9.54 |i 15.22 9.61 15.13 9.67 ; 15.14 9.74 18 19 16.11 10.07 11 16.07 10.14 16.02 10.21 15.98 10.28 19 20 16.96 10.60 ' 16.91 10.67 16.87 10.75 16.82 10.82 20 21 17.81 11.13 17.76 11.21 17.71 11.28 17.66 11.36 21 22 18.66 11.66 18.61 11.74 18.55 11.82 18.50' 11.90 22 23 19.51 12.19 19.45 12.27 19.40 12.36 19.34 12.44 23 24 20.35 12.72 20.30 12.81 20.24 12.90 ,20.18 12.98 24 25 21.20 13.25 21.14 13.34 21.08 13.43 21.03 13.52 25 26 22.05 13.78 21.99 13.87 21.93 13.97: 21.87 14.07 26 27 22.90 14.31 22.83 14.41 22.77 14.51 \ 22.71 14.61 27 28 23.75 14.84 23.68 14.94 23.61 15.04 1 23.55 15.15 28 29 24.59 15.37 24.53 15.47 24.48 15.58 24.39 15.69 29 30 25.44 15.90 25.37 16.01 ; 25.30 16.12 25.23 16.23 30 31 26.29 16.43 1 26 . 22 16.54 26.15 16.66 26.07 16.77 31 32 27.14 16.96 j 27.06 17.08 26.99 17.19 26.91 17.31 32 33 27.99 17.49 27.91 17.61 27.83 17.73 27.75 17.85 33 34 28.83 18.02 i 2S . 75 18.14 28.68 18.27 28.60 18.39 34 35 29.68 18.55 t 29.60 18.68 29.52 18.81 ' 29.44 18.93 35 36 30.53 19.08 30.45 19.21 30. 36 19.34 30.28 19.48 36 37 31.38 19.61 31.29 19.74 31.21 19.88 : 31.12 20.02 37 38 32.23 20.14 32.14 20.28 32.05 20.42! 31.96 20.56 38 39 33.07 20.67 32.98 20.81 32.89 20.95 32.80 21.10 39 40 33.92 21.20 33.83 21.34 33.74 34.58 21.49 33.64 21.64 40 41 41 34.77 21.73 1 34.67 21.88 22.03 34.48 22.18 42 35.62 22.26 35.52 22.41 35.42 22.57 35.32 22.72 42 43 36.47 22.79 ! 36.37 22.95' 36.27 23.10 36.16 23.26 43 44 37.31 23.32 : 37.21 23.48 37.11 23.64 37.01 23.80 44 45 38.16 23.85 1 38.06 1 24.01 37.95 24.18 37.85 24.34 45 46 39.01 24.38 38.90 124.55 { 38.80 24.72 |1 38.69 24.88 46 47 39.86 24.91 39.75 1 25.08 39.64 25.25 1-' 39.53 25.43 47 48 40.71 25.44 40.59:25.61 40.48 25.79 ii 40.37 25.97 48 49 41.55 25.97 i 41.44! 26.15 41.33 26.33 il 41.21 26.51 49 50 1 1 42.40 26.50 42.29 26.68 42.17 26.86 i Lat. i 42.05 27.05 50 Dep. Lat. Dep. Lat. Dep. Dep Lat. 1 .2 58 Deg. 571 Deg. 1! 57^ Deg. 57^ Deg. TRAVERSE TABLE. 67 I a . B s o 9 32 Deg. 324 Deg. 32i Deg. 321 Deg. P. a p ~51 Lat. Dep. Lat. Dep. Lat. Dep. 1 Lat. 42.89 Dep. 43.25 27.03 43.13 27.21 43.01 27.40 i 27.. 59 52 44.10 27.56 43.98 27.75 43.86 27.94 : 43.73 28.13 52 53 44.95 28.09 144.82 28.28 44.70 28.48 44.58 28.67 53 54 45.79 28.62 i! 45.67 28.82 45.54 29.01 1 45.42 29.21 54 55 46.64 29.15 46.51 29.35 46.39 29.55 i 46.26 29.75 55 56 47.49 29.68 i 47.36 29.88 47.23 30.09 47.10 .30.29 56 57 48.34 30.21 1 48.21 30.42 48.07 30,63 ! 47.94 30.84 57 58 49.19 30.74 i 49.05 30.95 48.92 31.16! 48.78 31.38 58 59 50.03 31.27 i 49.90 31.48 49.76 31.701; 49.62 31.92 59 60 61 50.88 31.80 ; 50.74 32.02 60.60 32.24 50.46 32.46 60 61 51.73 32.33; 51.59 32.55 51.45 32.78 51.30 33.00 6a 52.58 32.85 52.44 33.08 52.29 33.31 1 52.14 33.54 62 63 53.43 33.38 1 53.28 33.62 53.13 33.85 1 52.99 34.08 63 64 54.28 33.91 i 54.13 34.15 53.98 34.39 1 53.83 34.62 64 65 .55.12 34.44 54.97 34.68 54.82 34.92! 54.67 35.16 65 66 55.97 34.97 55.82 35.22 55.66 35.46 j 55.51 35.70 66 67 56.82 35.50 56.66 35.75 56.51 36.00 56.35 36.25 67 68 57.67 36.03 57.51 36.29 57.35 36.54 57.19 36.79 68 69 58.52 1 36.56 58.36 36.82 .58.19 37.07 58.03 37.33 69 70 1 .59.36 37.09 59.20 37.35 59.04 59.88 37.61 38.15 58.87 37.87 70 71 71 60.21 37.62 60.05 37.89 59.71 38.41 72 61.06 38.15 1 60.89 38.42 60.72 38.69 60.55 38.95 72 73 61.91 .38.68 61.74 38.95 61.57 39.22 61.40 39.49 73 74 62.76 39.21 62.58 39.49 62.41 39.76 62.24 40.03 74 75 63.60 39.74 63.43 40.02 63.25 40.30 63.08 40.57 75 76 64.45 40.27 64.28 40.55 64.10 40.83 63.92 41.11 76 77 65.30 40.80 65.12 41.09 64.94 41.37 64.76 41.65 77 78 66.15 41.33 65.97 41.62 65.78 41.91 65.60 42.20 78 79 67.00 41.86 66.81 42.16 66.63 42.45 166.44 42.74 79 80 81 67.84 42.39 67.66 42.69 67.47 42.98 ,67.28 43.28 43.82 80 81 68.69 42.92 68.50 43.22 68.31 43.52 i 68.12 82 69.54 43.45 69.35 43.76 69.16 44.06 '68.97 44.36 82 83 70.39 43.98 70.20 44.29 70.00 44.60 169.81 44.90 83 84 71.24 44.51 71.04 44.82 70.84 45.13 70.65 45.44 84 85 72.08 45.04 71.89 45.36 71.69 45.67 171.49 45.98 85 86 72.93 45.57 72.73 45.89 72.53 46.21 72.33 46.52 86 87 73.78 46.10 73.. 58 46.42 73.38 46.75 1 73.17 47.06 87 88 74.63 46.63 74.42 46.96 74.22 47.28 74.01 47.61 88 89 75.48 47.16 75.27 47.49 75.06 47.82 1 74.85 48.15 89 90 91 76.32 47.69 76.12 48.03 75.91 48.36 175.69 1 76.-53 48.69 90 91 77.17 48.22 76.96 48.56 76.75 48.89 49.23 92 78.02 48.75 77.81 49.09 77.59 49.43 77.38 49.77 92 93 78.87 49.28 78.65 49.63 78.44 49.97 78.22 50.31 93 94 79.72 49.81 79.50 50.16 79.28 50.51 79.06 50.85 94 95 80.56 50.34 80.34 50.69 80.12 51.04 79.90 51.39 95 96 81.41 50.87 81.19 51.23 80.97 51.58 80.74 51.93 96 97 82.26 51.40 82.04 51.76 81.81 52.12 81.58 52.47 97 98 : 83.11 51.93 82.88 52.29 82.65 52.66 82.42 .53.02 98 99 183.96 52.46 83.73 52.83 83.50 53.19 83.26 53.56 99 100 o \1 1 84.80 52.99 84.57 53.36 84.. 34 53.73 84.10 54.10 100 ! Dep. 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. 58 Deg. 571 Deg. 57i Deg. 57i Deg. R 68 TRAVERSE TABLE. 1 s o 33 Deg. 33^ Deg. 33^ Deg. 331 Deg, 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.84 0.54 0.84 0.55 0.83 0.55 0.83 0.56 1 2 1.68 1.09 1.67 1.10 1.67 1.10 1.66 1.11 2 3 2.52 1.63 2.51 1.64 2.50 1.66 2.49 1.67 3 4 3.35 2.18 3.35 2.19 3.34 2.21 3.33 2.22 4 5 4.19 2.72 4.18 2.74 4.17 2.76 4.16 2.78 5 6 5.03 3.27 5.02 3.29 5.00 3.31 4.99 3.33 6 7 5.87 3;8l 5.S5 3.84 5.84 3.86 5.82 3.89 7 8 6.71 4.36 6.69 4.39 6.67 4.42 6.65 4.44 8 9 7.. 55 4.90 7.53 4.93 7.50 4.97 7.48 5.00 9 10 11 8.39 5.45 8.36 5.48 8.34 5.52 6.07 8.31 5.. 56 10 11 9.23 5.99 9.20 6.03 9.. 17 9.15i 6.11 12 10.06 6.54 10.04 6.58 10.01 6.62 9.98 6.67 12 13 10.90 7.03 10.87 7.13 10.84 7.18 10.81 7.22 13 14 11.74 7.62 11.71 7.68 11.67 7.73 11.64 7.78 14 lo 12.58 8.17 12.54 8.22 12.51 8.28 12.47 8.33 15 16 13.42 8.71 13.38 8.77 13.34 8.83 13.30 8.89 16 17 14.26 9.26 14.22 9.32 14.18 9.38 14.13 9.44 17 18 15.10 9.80 15.05 9, 87 ! 15.01 9.93 14.97 10.00 1 18 I 19 15.93 10.35 15.89 10.^2 15.84 10.49 15.80 10.56 1 19! 20 21 16.77 10.89 11.44 16.73 10 rf?/ 16.68 11.04 16.63 11.11 20 17.61 17.56 11.51 17.51 11.59 17.46 11.67 21 22 18.45 11.98:1 18.40 12.06 18.35 12.14 18.29 12.22 22 23 19.29 13.53 1 19.23 12.61 19.18 j 12.69 19.12 12.78 23 24 20.13 13.07 20.07 13.16 20.01 ! 13.25 19.96 13.33 24 25 20.97 13.62 20.91 13.71 20.85 13.80 20.79 13.89 25 2fi 21.81 14.16 21.74 14.26 21.68 14.35 21.62 14.44 26 27 22.64 14.71 22 . 58 14. -80 22.51 14.90 22.45 15.00 27 28 23.48 15.25 23.42 15.35 23.35 15.45 23.28 15.56 28 29 24.32 15.79 24.25 15.90 24.18 16.01 24.11 16.11 29 30 31 25.16 16.34 25.09 16.45 25.02 16.56 24.94 16.67 30 31 26.00 16.88 25.92 17.00 25.85 17.11 25.78 17.23 32 26.84 17.43 26.76 17.55 26.68 17.66 26.61 17.78 32 33 27.68 17.97 27.60 18.09 27.52 18.21 27.44 18.33 33 34 28.51 18.52 23.43 18.64 28.35 18.77 28.27 18.89 34 35 29.35 19.06 29.27 19.19 29.19 19.. 32 29.10 19.44 35 36 30.19 19.61 .30.11 19.74 30.02 19.87 29.93 20.00 36 37 31.03 20.15 30.94 20.29 30.85 20.42 30.76 20.56 37 38 31.87 20.70 1 31.78 20.84 1 31.69 20.97 31.60 21.11 38 39 32.71 21.241 32.62 21.38 1 32,52 21.53 33.43 21.67 39 40 41 33.55 21.79 33.45 21.93 1 33.36 34.19 22.08 33.26 22.22 40 41 34.39 22.33 34.29 22.48 22.63 34.09 23.78 42 35.22 22.87 35.12 23.03 35.02 23.18 ; 34.92 23.33 42 43 36.06 23.42 35.96 23.58 35.83 23.73 1 35.75 23.89 43 44 36.90 23.96 36.80 24.12 36.69 24.29 i 36.58 24.45 44 45 37.74 24.51 37.63 24.67 37.52 24.84 37.42 25.00 45 46 38.58 25.05 38.47 25.22 .38.36 25.39 1 38.25 25.56 46 47 39.42 25.60 39.31 25.77 39.19 25.94! 39.08 26.11 47 48 40.26 26.14 40.14 26.32 40.03 23.49 39.91 26.67 48 49 41.09 26.69 40.98 26.87 40.86 27.04 40.74 27.22 49 50 i .2 41.93 27.23 41.81 27.41 41.69 27.60 1 41.57 27.78 50 Dep. Lat. Dep. Lat. Dep. L.t.t Dep. Lat. 6 o 1 5 57 Deg. 561 Deg. 56i Deg. 56\ Deg. TilAVliisrfi: TAEL£. 69 f- 33 Deg. 33^ Deg. 33i Deg. 33| Deg. s 9 D o CD 51 Lat. Dep. Lat. Dep. Lat. iiep. Lat. Dep. 42.77 27.78 42.65 27.96 42.63 28.15 42.40 i 28.33 1 51 52 43.61 28.32 43.49 28.51 43.36 28.70 43.24 28.89 i 52 53 44.45 28.87 44.32 29.06 44.20 29.25 44.07 29.45 53 54 45.29 29.41 45. i6 29. 6i 45.03 29.80 44.90 30.00 54 55 46.13 29.96 46.00 30.18 45.86 30.36 45.73 .30.56 55 56 46.97 30.50 46.83 30,70 46.70 30.91 46.56 31.11 56 57 47.80 31.04 47.67 31.25 47.53 31.46 47.39 31.67 1 57 58 48.64 31.59 48.50 31.80 48.37 32.01 48.23 32.22 58 59 49.48 32.13 49.34 32.35 49.20 32.66 49.06 32.78 59 • 60 61 50.32 51.16 32.68 50.18 32.90 50.03 33.12 49.89 j 33.33 60 61 33.22 51.01 33.45 50.87 33.67 50.72 ! 33.89 62 52.00 33.77 51.85 33.99 51.70 34.22 51.55 i 34.45 62 63 52.84 34.31 52.69 34.54 52.53 34.77 52.38 i 35.00 63 64 53.67 34.86 53.52 35.09 53.37 35.32 53.21 I 35.56 64 65 54.51 35.40 54.36 35.64 54.20 35.88 ; 54.05 ! 36.11 65 66 55.35 35.95 55.19 36.19 55.04 36.43 54.88 i 36.67 66 67 56.19 36.49 56.03 36.74 55.87 36.98 .55.71 ! 37.22 67 68 57.03 37.04 56.87 37.28 56.70 37.53 56.54! 37.78 68 69 57.87 37.58 57.70 37.83 57.54 38.08 ' 57.37 1 38.33 69 70 71 58.71 59.55 38.12 58.54 38.. 38 58.37 38.64:^ 58.20 ! 39.19 ' 59.03 ' 38.89 70 38.67 59.38 38.93 59.21 39.45 71 72 60.38 39.21 60.21 39.48 1 60.04 39.74 59.87 1 40.00 72 73 61.22 39.76 6.1.05 40.03: 60.87 40.29 60.70 j 40.56 73 74 62.06 40.30 61.89 40.57 61.71 40.84 61.53 1 41.11 74 75 62.90 40.85 62.72 41.13 62.. 54 4i.40 62.36 1 41.67 75 76 63.74 41.39 63.56 41.67 63.38 41.95 63.19 42.22 76 77 64.58 41.94 64.39 42.22 64.21 42.50 64.02 42.78 77 78 65.42 42.48 65 . 23 42.77 65.04 43.05 64.85 43.33 78 79 66.25 43.03 66.07 43.32 65.88 43.60 65.69 43.89 79 80 81 67.09 67.93 43.57 66.90 43.86 66.71 44.15 66.52 44.45 80 81 44.12 67.74 44.41 67.54 44.71 67.35 45.00 82 68.77 44.66 68.58 44.96 68.38 46.26 68.18 45.56 82 83 69.61 45.20 69.41 45.51 69.21 45. 8i 69.01 46.11 83 84 70.45 45.75 70.25 46.06 70.05 46.36 69.84 46.67 84 85 71.29 46.29 71.08 46.60 70.88 46.91 70.67 47.22 85 86 72.13 46.84 71.92 47.15 71.71 47.47 71. 5i 147.78 86 87 72.96 47.38 72.76 47.70 72.55 48.02 72.34 48.33 87 88 73.80 47.93 73.59 48.25 73.38; 48.57 73.17 48.89 88 89 74.64 48.47 74.43 48.80 74.22 49.12 74.00 49.45 89 90 91 75.48 49.02 7f,.27 49.35 75.05 49.67 74.83 50.00 90 91 76.32 49.56 76.10 49.89 75.88 50.23 75.66 50.56 92 77.16 50.11 76.94 50.44 76.72 50.78 76.50 51.11 92 93 78.00 .50.65 77.77 50.99 77.55 51.33 77.33 51.67 93 94 78,83 51.20 78.61 51.54 78.39 51.88 78.16 52.22 94 95 79,67 51.74 79.45 52.09 79.22 52.43 78.99 52.78 95 96 80.51 52.29 80.28 52.64 80.05 52.99 79.82 53.33 96 97 81.35 52.83 81.12 53.18 80.89 53.54 80.65 53.89 97 98 82.19 53.37 81.96 53.73 81.72 54.09 81.48 54.45 98 99 83.03 53.92 82.79 54.28 82.55 54.64 82.32 55.00 99 100 83.87 54.46 83.63 .54.83 83.39 55.19 83.15 55 . 56 100 o a Q Dep. Lat. Dep. Lat. Dep. Lat. Dep Lat. 57 Deg. 561 Deg. 561 Deg. 56i Deg, 70 TBAVEBSE TABLE. ii " 1! 1 34^ Deg. ji 34| Deg. i 34 Deg. |f 34i Deg. 5 Lat. Dep. !^ Lat. j Dep. ;' 1 Lat. j Dep. i Lat. Dep. 1 0.83 0.56: 0.83 0.56 : 0.82 i 0.57 i 0.82 1 0.57 1 2 1.66 1.12 i 1.65 1.13 ! 1.65 1.13,! 1^64 1,14 2 3 2.49 1.68 i| 2.48 1.69 ' 2.47 1.70 2.46 1.71 3 4 3.32 2.24;; 3.31 j 2.25 ! 3.30 2.27 3.29 2.28 4 5 4.15 2.80: 4.13 1 2.81 4.12 1 2.83 1 4.11; 2.85 5 6 4.97 3.36 ■ 4.96! 3.38 4.94 1 3.40 i| 4.93 1 3.42 6 7 5.80 3.91 ,; 5.79; 3.94 5.77 i 3.96 !l 5.75! 3.99 7 8 6.63 4.47 !i 6.61 4.50 6.59 I 4.53 ii 6.57 i 4.56 8 9 7.46 5.03;; 7.44 5.07 7.42 i 5.10 11 7.39! 5.13 9 10 11 8.29 5.59 ; 8.27 5.63 1 8.24 1 5.66 !j 8.22 ! 5.70 i 6.27 10 11 9.12 6.15 '■ 9.09! 6.19 ! 9.07 i 6.23 9.04 12 9.95 6.71 ! 9.92 6.75 ! 9.89 . 6.80 ' 9.86 ; 6.84 12 13 10.78 7.27 1 10.75 7.32 1 10.71 i 7.36 10.68 | 7.41 13 14 11.61 7.83 1 11.57 7.88 j 11.54 i 7.93 11. .50 i 7.98 14 15 12.44 8.39 : 12.40 1 8.44 112.36 8.50:12.32 8.55 15 16 13.26 8.95 13.23 i 9.00 i 13.19 9.06 ' 13.15 9.12 16 17 14.09 9.51 1 14.05 1 9.57 14.01 9.63! 13.97 9.69 17 18 14.92 10.07 14.88 110.13 i 14.83 10.20 14.79 ; 10.26 18 19 15.75 10.62 15.71110.69 : 15.66 10.76 15.61110.83 19 20 16.53 11. IS 16.531 11.26 17.36 1 11.82 16.43 11.33 16.43 17.25 ' 11.40 20 21 17.41 11.74 17.31 1 11.89 : 11.97 21 22 ! 18.24 12.30 18.18 i 12.38 18.13 112.46 18.08! 12.54 22 23 i 19.07 12.86 19.01 12.94 18.95! 13.03 18.90 113.11 23 24 19.90 13.42 i 19.84; 13.51 , 19.78 1 13.59 19.72 ! 13.68 24 25 20.73 13.98 1 20.66; 14.07 i 20.60 1 14.16 20.. 54 I 14.25 25 26 21.55 14.54 121.49 14.63 21.43 1 14.73 21.36 i 14.82 26 27 22.38 15.10 122.32 ! 15.20 22.25 i 15.29 22.18 1 15.39 27 28 23.21 15 66 123.14 15.76 23. OS j 15.86 23.01 i 15.96 28 29 24.04 16.22 1 23.97: 16.32 23.90 1 16.43 23.83 1 16.53 29 30 24.87 16.78 : 24.80! 16.88 : '25.62' 17.45 24.72 1 16.99 24.65 ! 17.10 30 31 25.70 17.33 25 . 55 17.56 25.47 ! 17.67 31 32 26.53 17.89 26.45 13.01 26.37 18.12 26.29 j 18.24 32 33 27.36 18.45 27.28 1 18.57: 27.20 18.69 27.11 18.81 33 34 28.19 19.01 ,28.10.; 19.14; 28.02 19.26 ! 27.94 19.33 34 35 29.02 19.57 28.93! 19.70 : 28.84 19.82 28.76 19.95 35 36 29.85 20.13 29.76 i 20.26 29.67 20.39 ; 29.58 20.. 52 36 37 30.67 20.69 30.58; 20.82 30.49 20.96 30.40 21.09 37 38 31.50 21.25 , 31.41 21.39 31.32 21.52 31.22 21.66 38 39 32.33 1 21.81 32.24 21.95! 32.14 22.09 32.04 i 22.23 39 40 33.16' 22.37 ' 33.06 22.51 1 33.89 23.07 1 32.97 1 22.66 32.87 33.69 22.80 40 41 i 33.99 22.93 : 33.79 i 23.22 i 23.37 41 42 j 34.82 23.49 34.72 23.64! 34.61 j 23.79! 34.51 ; 23.94 1 42 43 35.65 24.05 35.54 24.20 1 35.44 24.36 35.33 124.51 43 44 36.48 24.60 , 36.37 24.70! 36.26 24.92 36.15 125.08 44 45 37.31 25.16 37 . 20 25 . 33 : 37.09 25.49 36.97 125.65 45 46 38.14 25.72 38.02 25.89 j 37.91 26.05 37.80 i 26.22 46 47 38.96 26.28 38.85 26.45 1 38.73 26.62 38.62 ! 26.79 47 48 39.79 26.84 39.68 27.01 i 39.56 27.19 i 39.44 27.36 48 49 40.62 27.40 40. .50 27.58) 40.38 27.75! 40.26 27.93 49 50 41.45 27.96 41.33 28.14 1 41.21 28.32 41.08 28.50 50 Dep. Lat. 1 Dep. Lat. Dep. Lat. Dep. Lat. c s .2 1 56 1 )eg. 55| Deg. 55^ Deg. 5.3i Deg. TRAVERSE TABLE. 71 o GD 3 ? 51 34 Deg. 34i Deg. 34A Deg. 34^ Deg. 1 ? 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 42.28 28.. 52 42.16 28.70 42.03 28.89 41.90 29.07 52 43.11 29.08 42.98 29.27 42.85 29.45 42.73 29.64 52 53 43.94 29.64 43.81 29.83 i 43.68 1 30.02 43.55 30.21 63 54 44.77 30.20 44.64 30.39 44.50 30.59 44.37 30.78 64 55 45.60 30.76 45.46 30.95 45.33 31.15 45.19 31.35 55 56 46.43 31.31 46.29 31.52 46.15 31.72 46.01 31.92 56 57 47.26 31.87 47.12 32.08 46.98 32.29 46.83 32.49 57 58 48.08 32.43 47.94 32.64 47.80 32.85 47.66 33.06 58 59 48.91 32.99 48.77 33.21 48.62 33.42 48.48 33.63 59 60 61 49.74 33.55 49.60 33.77 49.45 33.98 49.30 34.20 60 61 50.57 34.11 50.42 34.33 50.27 34.55 50.12 34.77 62 51.40 34.67 51.25 34.89 51.10 35.12 50.94 35.34 62 63 .52.23 35.23 52.08 .35.46 51.92 35.68 51.76 35.91 63 64 53.06 35.79 52.90 36.02 52.74 36.25 52.59 36.48 64 65 53.89 36.35 53.73 36.58 53.57 36.82 .53.41 37.05 65 66 54.72 36.91 54.55 37.15 54.39 37.38 54.23 37.62 66 67 55 . 55 37.46 .55.38 37.71 55.22 37.95 55.06 38.19 67 68 56.37 38.03 56.21 38.27 56.04 38.52 55.87 38.76 68 69 57.20 38.58 57.03 38.83 56.86 39.08 56.69 39.33 69 _70 71 .58.03 58.86 39.14 57.86 58.69 39.40 39.96 57.69 39.65 57.52 58.34 39.90 40.47 70 71 39.70 58.51 40.21 72 59.69 40.26 59.51 40.. 52 59.34 40.78 59.16 41.04 72 73 60.52 40.82 60.34 41.08 60.16 41.35 59.98 41.61 73 74 61.35 41.38 61.17 41.65 60.99 41.91 60.80 42.18 74 75 62.18 41.94 61.99 42.21 61.81 42.48 61.62 42.75 75 76 i 63.01 142.50 1 62.82 42.77 62.63 43.05 62.45 43.32 76 77 63.84 43.06 63.65 43.34 63.46 43.61 63.27 43.89 77 78 64.66 43.62 64.47 43.90 64.28 44.18 64.09 44.46 78 79 65.49 44.18 65.30 44.46 65.11 44.75 64.91 45.03 79 80 66.32 44.74 66.13 45.02 45.59 65.93 45.31 65.73 45.60 80 81 81 67.15 45.29 66.95 66 . 75 45.88 66.55 46.17 82 167.98 45.85 67.78 46.15 67.58 46.45 67.37 46.74 82 83 68.81 46.41 68.61 46.71 68.40 47.01 68.20 47.31 83 84 69.64 46.97 69.43 47.28 69.23 47.58 69.02 47.88 84 85 70.47 4 7.. 53 70.26 47.84 70.05 48.14 69.84 48.45 85 86 71.30 148.09 71.09 48.40 70.87 48.71 70.66 49.02 86 87 72.13 148.65 71.91 48.96 71.70 49.28 71.48 49.59 87 88 72.96 49.21 72.74 49.53 72.52 49.84 72.30 50.16 88 89 73.78 49.77 73.57 50.09 73.35 .50.41 1 73.13 50.73 89 90 91 74.61 50.33 74.39 50.65 74.17 50.98 73.95 51.30 90 91 75.44 50.89 75.22 51.22 75.00 51.54 74.77 51.87 92 76.27 51.45 76.05 51.78 75.82 52.11 75.59 52.44 92 93 77.10 52.00 76.87 52.34 76.64 52.68 1 76.41 53.01 93 94 77.93 52.56 77.70 52.90 77.47 53.24 77.23 53.58 94 95 78.76 53.12 78,53 53.47 78.29 53.81 78.06 54.15 9n 96 79.59 53.68 79.35 54.03 79.12 54.37 78.88 54.72 96 97 80.42 54.24 80.18 54.59 79.94 54.94 79.70 55.29 97 98 81.25 54.80 81.01 .55.15 80.76 55.51 80.52 55.86 98 99 82.07 55.36 81.83 55.72 81.59 56.07 81.. 34 56.43 99 lOO o3 o c: CD Q 82.90 55.92 82.66 56.28 82.41 56.64 82.16 57.00 100 § Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 56 Deg. 55| Deg. 55i Deg. 55i Deg. 72 TRAVERSE TABLE. 9 35 Deg. 35i Deg. 35i Deg. 35| Deg. o Lat. Dep. Lat. 0.82 Dep. Lat. Dep. Lat. Dep. 1 0.82 0.57 0.58 0.81 0.58 0.81 0.58 1 2 1.64 1.15 1.63 1.15 1.63 1.16 1.62 1.17 2 3 2.46 1.72 2.45 1.73 2.44 1.74 2.43 1.75 3 4 3.28 2.29 3.27 2.31 3.26 2.32 3.25 2.34 4 5 4.10! 2.87 4.08 2.89 4.07 2.90 4.06 2.92 5 6 4.91 ; 3.44 4.90 3.46 4.88 3.48 4.87 3.51 6 7 5.73 i 4.01 5.72 4.04 5.70 4.06 6.68 4.09 7 8 6.55 1 4.59 6.53 4.62 6.51 4.65 6.49 4.67 8 9 7.37 5.16 7.35 5.19 7.33 5.23 7.30 5.26 9 10 11 8.19 5.74 8.17 5.77 8.14 5.81 8.12 5.84 10 9.01 6.31 8.98 6.35 8.96 6.39 8.93 6.43 11 12 9.83 6.88 9.80 6.93 9.77 6.97 9.74 7.01 12 13 10.65 7.46 10.62 7.50 10.. 58 7.55 10.55 7.60 13 14 11.47 8.03 11.43 8.08 11.40 8.13 11.36 8.18 14 15 12.29 8.60 12.25 8.66 12.21 8.71 12.17 8.76 15 16 13.11 9.18 13.07 9.23 13.03 9.29 12.99 9.35 16 17 13.93 9.75 13.88 9.81 13.84 9.87 13.80 9.93 17 18 14.74 10.32 14.70 10.39 14.65 10.45 14.61 10.52 18 19 15.56 10.90 15.52 10.97 15.47 11.03 15.42 11.10 19 20 21 16.38 17.20 11.47 16.33 11.54 16.28 11.61 16.23 11.68 20 12.05 17.15 12.12 17.10 12.19 17.04 12.27 21 22 18.02 12.62 17.97 12.70 17.01 12.78 17.85 12.85 22 23 18.84 13.19 18.78 13.27 18.72 13.36 18.67 13.44 23 24 19.66 13.77 19.60 13.85 1 19.54 13.94'' 19.48 14.02 24 25 20.48 14.34 20.42 14.43 20.35 14.52 20.29 14.61 25 26 21.30 14.91 21.23 15.01 1 21.17 15.10 21.10 15.19 26 27 22.12 15.49 22.05 15.58 1 ■21.98 15.68 : 21.91 15.77 27 28 22.94 16.06 23.87 16.16 22.80 16.26 22.72 16.36 28 29 23.76 16.63 23.68 16.74 23.61 16.84^23.54 16.94 29 30 24.57 17.21 24.50 17.31 24.42 17.42 24.35 17.53 30 31 25.39 17. 7S 25 . 32 17.89 25.24 18.00 25.16 18.11 31 32 26.21 18.35 26.13 18.47 26.05 18.58 , 25.97 18.70 33 33 27.03 18.93 26.95 19.05 26.87 19.16 '26.78 19.28 33 34 27.85 19.50 27.77 ]9.62 27.68 19.74! 27.59 19.86 34 35 28.67 20.08 28.58 20.20 28.49 20.32 ,28.41 20.45 35 36 29.49 20.65 29.40 20.78 29.31 20.91 129.22 21.03 36 37 30.31 21.22 .30.22 21.35 30.12 21.49 130.03 21.62 37 38 31.13 21.80 31.03 21.93 30.94 22.07 i 30.84 22.20 38 39 31.95 22.37 31.85 22.51 31.75 22.65 j 31.65 22.79 39 40 32.77 22.94 32.67 23.09 32.56 23.23 j 32.46 33.27 23.37 40 41 33.59 23.52 33.48 23.66 33.38 23.81 23.95 41 42 34.40 24.09 34.30 24.24 34.19 24.39 134.09 24.54 42 43 35.22 24.66 35.12 24.82 35.01 24.97 1 34.90 25.55 |!35.71 25.12 43 44 36.04 25.24 35.93 25.39 35.82 25.71 44 45 36.86 25.81 36.75 25.97 36.64 26.13 i 36.52 26.29 45 46 37.68 26.38 37.57 26.55 37.45 26.71 37.33 26.88 46 47 38.50 26.96 38.38 27.13 38.26 27.29 38.14 27.46 47 48 39.32 27.53 39.20 27.70 .39.08 27.87 38.96 28.04 48 49 40.14 28.11 40.02 28.28 39.89 28.45 39.77 28.63 49 50 40.96 28.68 40.83 28.86 40.71 29.04 40.58 29.21 50 to Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 6 o c S .22 Q 55 Deg. 541 Deg. 54^ Deg. 54i Deg. TRAVERSE TABLE. 73 5 p s p 51 35 Deg. 35i Deg. 35i Deg. 35| Deg. o CD Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 41.78 29.25 41.65 29.43 41.52 29.62 41.39 29.80 51 52 42.60 29.83 42.47 30.01 42.33 30.20 42.20 30.38 52 53 43.42 30.40 43.28 30.59 43.15 30.78 43.01 30.97 53 54 44.23 30.97 44.10 31.17 43.96 31.36 43.82 31.55 54 55 45.05 31.55 44.92 31.74 44.78 31.94 44.64 32.13 55 56 45.87 32.12 45.73 32.32 145.59 32.52 45.45 32.72 56 57 46.69 32.69 46.55 32.90 46.40 33.10 46.26 33.30 57 58 47.51 33.27 47.37 33.47 47.22 33.68 i 47.07 33.89 58 59 48.33 33.84 48.18 34.05 48.03 34.26 47.88 34.47 59 60 61 49.15 .34.41 49.00 34.63 48.85 34.84 : 48 . 69 35.05 60 49.97 34.99 49.82 35.21 49.66 35.42 49.51 35.64 61 62 50.79 35.56 50.63 35.78 .50.48 36.00 : 50.32 38.22 62 63 51.61 .36.14 51.45 36.36 51.29 36.58 51.13 36.81 63 64 52.43 36.71 52.27 36.94 52.10 37.16 51.94 37.39 64 65 53.24 37.28 53.08 37.51 152.92 37.75 52.75 37.98 65 66 54.06 37.86 53.90 38.09 53.73 ,38.. 33 ,53.56 38.56 66 67 54.88 38.43 .54.71 38.67 54.55 38.91 54.38 39.14 67 68 55.70 39.00 55.53 39.^5 55.36 39.49 55.19 39.73 68 69 56.52 39.58 56.35 39.82 56.17 40.07 56.00 40.31 69 70 71 57.34 40.15 57.16 40.40 56.99 40.65 56.81 40.90 70 71 58.16 40.72 57.98 40.98 57.80 41.23 57.62 41.48 72 58.98 41.30 58.80 41., 55 58.62 41.81 .58.43 42.07 72 73 .59.80 41.87 .59.61 42.13 1 59.43 42.39 59.24 42.65 73 74 60.63 42.44 60.43 42.71 60.24 42.97 60.06 43.23 74 75 61.44 43.02 61.25 43.29 61.06 43.55 60.87 43.82 1 75 j 76 62.26 43.59 62.06 43.86 61.87 44.13 61.68 44.40 ' 76 77 63.07 44.17 62.88 44.44 62.69 44.71 62.49 44.99, 77 1 78 63.89 44.74 63.70 45.02 63.50 45.29 63.30 45.57 78 79 64.71 45.31 64.51 45.59 64.32 45.88 64.11 46.16 79 80 81 65.. 53 45.89 65.33 66.15 46.17 46.75 65.13 46.46 64.93 65.74 46.74 80 81 66.35 46.46 65.94 47.04 47.32 82 67.17 47.03 66.96 47.33 66.76 47.62 66.55 47.91 82 83 67.99 47.61 67.78 47.90 67.57 48.20 67.36 48.49 83 84 68.81 48.18 68.60 48.48 68.39 48.78 68.17 49.08 84 85 69.63 48.75 69.41 49.06 69.20 49.36 68.98 49.66 85 86 70.45 49.33 70.23 49.63 70.01 49.94: 69.80 50.25 86 87 71.27 49.90 71.05 .50.21 70.83 50.. 52 70.61 50.83 87 88 72.09 50.47 171.86 50.79 71.64 51.10; 71.42 51.41 5^.00 88 89 72.90 51.05 1 72.68 51.37 72.46 51.68 72.23 89 90 91 73.72 51.62 i 73.-50 51.94 73.27 52. 2G 73.04 .52.58 90 74.54 52.20 74.31 52.52 74.08 ,52.84 73.85 53.17 91 92 75.36 52.77 75.13 53.10 74.90 53.42 74.66 53.75 92 93 76.18 .53.34 75.95 53.67 75.71 54.01 75.48 54.34 93 94 77.00 53 . 92 76.76 54.25 76.. 53 54., 59 ' 76.29 54.92 94 95 77.82 54.49 77.58 54.83 77.34 55.17! 77.10 55.50 95 96 78.64 55.06 78.40 ,55.41 78.16 55.75 77.91 56.09 96 97 79.46 55.64 79.21 55.98 78.97 56.33 78.72 56.67 97 98 80.28 56.21 80.03 56.. 56 79.78 56.91 ; 79.53 57.26 98 99 81.10 56.78 80.85 57.14 80.60 57.49 ; 80.35 57.84 99 100 i .2 Q 81.92 .57.36 81.66 57.71 81.41 58.07 81.16 58.42 100 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 55] Deg. 541 Deg. 54i Deg. 1 54i Deg. C y. D»a:. "iroi *:^ 3F l.fiS I.L^ JitEte?. LoiL. Bteg^ ' Li^ ■ Dep, L.SI 3.23; 4.13 3bfDeff. 1.:- L.T" 2.S7 3.3a 4.14 4.T3 3.33 5.SL 4.«S 4.e i.S3 5.«4 I.I* LIS 3.38 S.ST 3.3? 5.9& f»:t DesT- La.^ EXepv S.« 3.a» 4.9II (S.^li i.aifi 3.39 1 Of* ? . i" 21 14. 3*^ Ii.34r 32 :~ -■• :• -^ 23 at 25 as i.It) 7.17 7.r .- 5.^ «. m,<)*J 24. 42 53 7*^ 24 "55? ?t? ^"^ 24 !5 24.53 ! 41 LiL D^. ! Lar-^ | IVc :3l S& 55^ Dear. 5 TEAVERSE TABLE. 75 2 {3 P 51 36 Deg. 364 Deg. 36i Deg. 361 Deg. D 5- o ? ~51 Lat. Dep. Lat. Dep. Lat. Dep. Lai. Dep. 41.26 29.98 41.13 30.16 41.00 30.34 40.86 30.51 52 42.07 30.56 41.94 30.75 41.80 30.93 41.67 31.11 52 53 42.88 31.15 42.74 31.34 42.60 31.63 42.47 31.71 53 54 43.69 31.74 43.55 31.93 43.41 32.12 43.27 32.31 54 55 44.50 32.33 44.35 32.52 44.21 32.72 44.07 32.91 66 56 45.30 32.92 45.16 33.11 45.02 33.31 44.87 33.51 56 57 46.11 33.50 45.97 33.70 45.82 33.90 45.67 34.10 57 58 46.92 34.09 46.77 34.30 46.62 34.50 46.47 34.70 58 69 47.73 34.68 47.58 34.89 47.43 35 09 47.27 35.30 69 60 61 48.54 35.27 48.39 35.48 48.23 36.69 48.08 48.88 35.90 60 61 49.35 35.85 49.19 36.07 49.04 36.28 36.50 62 50.16 36.44 50.00 36.66 49.84 36.88 49.68 37.10 62 63 .50.97 37.03 150.81 37.25 50.64 37.47 50.48 37.69 63 64 51.78 37.62 51.61 37.84 51.45 38.07 51.28 38.29 64 65 52.59 38.21 52.42 38.44 52.25 38.66 52.08 38.89 65 66 53.40 38.79 1 53.23 39.03 53.05 39.26 52.88 39.49 66 67 54.20 39.38 54.03 39.62 53.86 39.85 53.68 40.09 67 68 55.01 39.97 ! 54.84 40.21 54.66 40.45:154.49 40.69 68 69 55.82 40.56 ! 55.64 40.80 55.47 41.04 155.29 41.28 69 70 71 56.63 41.14 : 56.45 41.39 56.27 41.64 i 56.09 56.89 41.88 70 71 57.44 41.73 57.26 41.98 57.07 42.23 42.48 72 58.25 42.32 58.06 42. 5» 57.88 42.83 ;i 57.69 43.08 72 73 59.06 42.91 .58.87 43.17 .58.68 43.42 58.49 43.68 73 74 59.87 43.50 |, 59.68 43.76 59.49 44.02 59.29 44.28 74 75 60.68 44.08 60.48 44.35 60.29 44.61 60.09 44.87 75 76 61.49 44.67 61.29 44.94 61.09 45.21 60.90 45.47 76 77 62.29 45.26 62.10 45.53 61.90 45.80 61.70 46.07 77 78 63.10 45.85 62.90 46.12 62.70 46.40 62.50 46.67 78 79 63.91 46.43 63.71 46.71 63.. 50 46.99 63.30 47.27 79 80 81 64.72 47.02 64.52 47.30 64.31 47.59 64.10 47.87 80 81 65.53 47.61 65.32 47.90 65.11 48.18 64.90 48.46 82 66.34 48.20 66.13 48.49 65.92 48.78 65.70 49.06 82 83 67.15 48.79 66.93 49.08 66 . 72 49.37 66.50 49.66 83 \ 84 67.96 49.37 67.74 49.67 67.52 49.97 67.3] 50.26 84 ' 85 68.77 49.96 68.55 50.26 68.33 50.56 68.11 50.86 85 86 69.. 58 50.55 69.35 50.85 69.13 51.15 68.91 51.46 86 87 70.38 51.14 70.16 51.44 69.94 51.75 69.71 1 52.05 87 88 71.19 51.73 70.97 52.04 70.74 52.34 70.51 1 52.65 88 89 72.00 52.31 71.77 52.63 71.54 52.94 71.31 53 . 25 89 90 91 72.81 52.90 72.58 53.22 72.35 53.53 72.11 53.85 90 91 73.62 53.49 1 73.39 53.81 73.15 54.13 72.91 54.45 92 74.43 54.08 74.19 54.40 73.95 54,72 73 . 72 55.05 92 93 75.24 54.66 75.00 54.99 74.76 55.32 74.. 52 55.64 93 94 76.05 55.25 75.81 55.58 75.56 .55.91 75.32 56.24 94 95 76.86 55.84 76.61 56.17 76.37 56.51 76.12 56.84 95 96 77.67 56.43 77.42 56.77 77.17 57.10 76.92 57.44 96 97 78.47 57.02 78.23 57.36 77.97 57.70 77.72 58.04 97 98 79.28 57.60 79.03 57.95 78.78 58.29 78.. 52 58.64 98 99 80.09 58.19 79.84 58.54 79.58 58.89 79.32 59.23 99 100 i a S tn 80.90 58.78 80.64 59.13 Lat, 80.39 59.48 80.13 59.83 100 Dep. Lat. Dep. Dep. Lat. Dep Lat. 54 Deg. 531 Deg. 634 Deg 53i Deg, 76 TRAVERSE TABLE o s o CO 1 \ 37 Deg. m Deg. 37iDeg. 37 f Deg, 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat, Dep. 0.80 0.60 1 0.80 0.61 0.79 0.61 0.79 0.61 1 2 1.60 1.20 1.59 1.21 1.59 1.33 1.58 1.23 2 3 2.40 1.81 2.39 1.82 2.38 1.83 2.37 1.84 3 4 3.19 2.41 3.18 2.43 3.17 2.43 3.16 3.45 4 6 3.99 3.01 3.98 3.03 3.97 3.04 3.95 3.06 5 6 4.79 3.61 4.78 3.63 4.76 3.65 4.74 3.67 6 7 5.59 4.21 5.57 4.34 5.. 55 4.36 5.53 4.39 7 8 6.39 4.81 6.37 4.84 6.35 4.87 • 6.33 4.90 8 9 7.19 5.42 7.16 5.45 7.14 5.48 7.12 5.51 9 10 li 7.99 6.02 7.96 6.05 7.93 6.09 7.91 6.12 10 11 8.78 6.62 8.76 8.66 8.73 6.70 8.70 6.73 13 9.58 7.32 9.55 7.36 9.52 7.31 9.49 7.35 12 13 10.38 7.83 10.35 7.87 10.31 7.91 10.28 7.96 13 14 11.18 8.43 11.14 8.47 11.11 8.. 53 11.07 8.57 14 15 11.98 9.03 11.94 9.08 11.90 9.13 11.86 9.18 15 16 12.78 9.63 1 12.74 9.68 12.69 9.74 12.65 9.80 16 17 13.58 10.33 13.53 10.29 13.49 10.35 13.44 10.41 17 18 14.33 10.83 1 14.33 10.90 14.28 10.96 14.23 11.02 18 19 15.17 11.43! 15.12 11. .50 15.07 11.57 1 15.02 11.63 19 20 31 15.97 12.04 15.92 12.11 15.87 16.68 13.18 ! 15.81 12.24 20 16.77 12.64 16.73 13.71 13.78 1 16.60 12.86 21 22 17.57 13.24 17.51 13.33 17.45 13.39 17.40 13.47 22 23 18.37 13.84 1 18.31 13.93 18.35 14.00 18.19 14.08 33 24 19.17 14.44, 19.10 14.53 19.04 14.61 18.98 14.69 34 35 19.97 15.05 19.90 15.13 19.83 15.33 19.77 15,31 35 26 20.76 15.65 20.70 15.74 30.63 15.83 20.56 15.92 26 27 31.56 16.25 21.49 16.-34 31.43 16.44 21.35 16.53 27 28 22.36 16.85 33.39 16.95 -32.21 17.05 33.14 17.14 28 39 23.16 17.45 33.08 17.55 23.01 17.65 33.93 17.75 29 30 "31 33.96 24.76 18.05 23.88 18.16 18.76 33.80 18.26 33.73 18.37 30 31 18.06 24.68 24.59 18.87 34.51 j 18.98 32 25.56 19.26 25.47 19.37 25.39 19.48 35.30 19.59 32 33 26.35 19. 8G 26.27 19.97 26.18 20.09 36.09 20.20 33 34 27.15 20.46 27.06 30.53 26.97 20.70 36.88 30.82 34 35 27.95 21.06 27.86 31.19 37.77 21.31 37.67 21.43 35 36 28.75 21.67 28.66 31.79 28.. 56 21.92 28.46 22.04 36 37 29.55 22.27 29.45 33.40 39.35 23.53 29.36 33.65 37 38 30.35 33,87 30.25 33.00 30.15 33.13 30.05 23.36 38 39 31.15 33.47 31.04 33.61 30.94 33.74 30.84 33.88 39 40 41 31.95 34.07 31.84 34.31 34.82 31.73 24.35 31.63 34.49 40 41 32 . 74 34.67 32.64 33.53 24.98 33.42 35.10 42 33.54 35,38 33.43 25.42 33.33 25.57 33.31 35.71 43 43 34.34 25 . 88 34.23 36.03 34.11 26.18 34.00 26.33 43 44 35.14 26.48 35.02 26.63 34.91 26.79 34.79 26.94 44 45 35.94 27.08 35.82 27.24 .35.70 27.39 35.58 27.55 45 46 36.74 37.68 36 . 62 27.84 36.49 28.00 36.37 38.16 48 47 37.54 28.29 37.41 28.45 37.39 28.61 37.16 28.77 47 48 38.33 28.89 38.21 29.05 38.08 29.23 37.95 29.39 48 49 39.13 39.49 39.00 29.66 38.87 29.83 38.74 30.00 49 50 39.93 30.09 39.80 Dep. 30.26 39.67 30.44 39.53 30.61 50 Dep. Lat. Lat Dep. Lat. Dep. Lat. CD U a 1 53 Deg. 52f Deg. 52i Deg 52i Deg. TK AVERSE TABLE. 77 i n ? 51 37 Deg. 37i Deg. 21h Deg. 371 Deg. e a ? "61 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 40.73 30.69 40.60 30.87 40.46 31.05 40.. 33 31.22 52 41.53 31.29 41.39 31.48 41.25 31.66 41.12 31.84 62 53 42.33 31.90 42.19 32.08 42.05 .32.26 41.91 32.45 63 54 43.13 32.50 42.98 32.69 42.84 32.87 42.70 33.06 54 55 43.92 33.10 43.78 33.29 43.63 33.48 43.49 33.67 56 56 44.72 33.70 44.58 33.90 44.43 34.09 44.28 34.28 56 57 45.62 34.30 45.37 34.50 45.22 34.70 45.07! 34.90 57 68 46.32 34.91 46.17 35 . 1 1 46.01 35.31 45.86 35.51 58 59 47.12 35.51 46.96 35.71 46.81 35 . 92 46.65 36.12 59 60 61 47.92 36.11 47.76 36.32 47.60 36.53 37.13 47.44 48.23 36.73 60 61 48.72 36.71 48.56 36.92 48.39 37.35 62 49.52 37.31 49.35 37.. 53 49.19 37.74 49.02 37.96 62 63 50.31 37.91 50.15 38.13 49.98 38.36 49.81 38.57 63 64 51.11 38.. 52 50.94 38.74 50.77 38.96 50.60 .39.18 64 65 51.91 39.12 51.74 39.34 61.57 39 . 57 51.39 39.79 65 66 52.71 39.72 52.54 39.95 52.36 40.18 52.19 40.41 66 67 53.51 40.32 53.33 40.55 53.15 40.79 .52.98 4i.02 67 68 54.31 40.92 .54.13 41.16 53.96 41.40 53.77 41.63 68 69 55.11 4i.53 54.92 41.77 54.74 42.00 54.56 42.24 69 70 71 55.90 56.70 42.13 42.73 55.72 56.52 42.37 42.98 55.53 56.33 42.61 55.35 42.86 70 71 43.22 56.14 43.47 73 67.50 43.33 57.31 43.68 57.12 43.83 66.93 44.08 72 73 58.30 43.93 1 .58.11 44.19 57.91 44.44 57.72 44.69 73 74 59.10 44.53 58.90 44.79, 58.71 45.05 68.61 45.30 74 75 59.90 45.14 159.70 46.40 .59.50 45 . 66 59 . .30 45.92 75 76 60.70 45. 74 160.. 50 46.00 60.29 46.27 60.09 46.63 76 77 61.49 4^.34 I 61.29 46.61 61.09 46.87 60.88 47.14 77 78 62.29 46.94; 62.09 47.21 61.88 47.48 61.67 47.75 78 79 63.09 47.54; 62.88 47.82 62.67 48.09 62.46 48.37 79 80 81 63.89 64.69 48.15; 48.75; 63.68 48.42 49.03 63.47 64.26 48.70 49.31 63.20 48.98 80 8l 64.48 64.05 49.59 82 65.49 49.35 1 66.27 49.63 65.05 49.92 64.84 50.20 82 83 66.29 49.95! 66.07 .50.24 65.85 50.53 65.63 50.81 83 84 67.09 50.55 66.86 .50.84 66.64 51.14 66.42 51.43 84 85 67.88 61.151 07.66 51.45 67.43 61.74 67.21 52.04 85 86 68.68 51.76; 68.46 62.06 68.23 i 52.35 68.00 52.65 86 87 69.48 52.36! 69.25 52.66 69.02 62.96 68.79 .53.26 87 88 70.28 52.96 11 70.05 53.27 69.82 63.57 69.58 53.88 88 89 71.08 53.56 70.84 53.87 70.61 54.18 70.37 54.49 89 90 '91 71.88 72. 6« 54.16 ,54.77 71.64 64.48 56.08 71.40 54 . 79 71.16 55.10 90 72.44 72.20 55.40 71.95 .55.71 " 91 92 73.47 55.37 73.23 55.69 72.99 56.01 72.74 .56.32 92 93 74.27 55.97 74.03 56.29 73.78 56.61 73.. 53 56.94 93 94 75.07 56.57 74.82 i 56.90 74.. 58 67.22 74.32 57.. 55 94 96 75.87 57.17 75.62 1 67.50 75.37 67.83 75.12 58.16 95 96 76.67 57.77 76,42 68.11 76.16 58.44 75.91 58.77 96 97 77.47 58.38 77.21 58.71 76.96 59.06 76.70 59.39 97 98 78.27 58.98 78.01 69.32 77.75 59.66 77.49 60.00 98 99 79.06 .59.58 78.80 59.92 78.64 60.27 78.28 60.61 99 100 79.86 60.18 79.60 60.53 79.34 60.88 79.07 61.22 100 Dep. Lat. Dep. Lat. Dep Lat. Dep. Lat. a 1 3 53 1 )eg. 521 Deg. ^,_ 52h Deg. I 52i Deg. 78 TEAVEESE TABLE. a 5' 1 38 Deg. m Deg. 38^ Deg. 381 Deg. 1 Lat. Dep. Lat. Dep. Lat. 1 Dep. Lat. Dep. 1 0.79! 0.62 0.79 0.62 0.78! 0-62 0.78 0.63 1 2 1.58; 1.23 1.57 1.24 1.57 1.24 1..56 1.25 2 3 2.36 1.85 2.36 1.86 2.35 1.87 2.34 1.88 3 4 3.15; 2.46 3.14 2.48 3.13 2.49 3.12 2.50 4 5 3.94 3.08 3.93 3.10| 3.91 I 3.11 3.90 3.13 5 6 4.73 3.69 4.71 3.71 1 4.70! 3.74 4.68 3.76 6 7 5.52 4.31 5.50 4.33 5.48! 4.36 5.46 4.38 7 8 6.30 4.93 6.28 4.95 6.26 1 4.98 6.24 5.01 8 9 7.09 5.54 7.07 5.57 7.04 1 5.60 7.02 5.63 9 iO 11 7.88 6.16 7.85 6.19 7.83 6.23 7.80 6.26 10 8.67 6.77 8.64 6.81 8.61 : 6.851 8.58 6.89 11 12 9.46 7.39 9.42 7.43 9.39 7.47 9.36 7.51 12 13 10.24 8.00! 10.21 8.05 10.17 8.09 10.14 8.14 13 14 11.03 8.62! 10.99 8.67 10.96 8.72 10.92 8.76 14 15 11.82 9.23' 11.78 9.29 1 11.74! 9.34 11.70 9.39 15 16 12.61 9.85 12.57 9.91 1 12.52! 9,96 1 12.48 10.01 16 17 13.40: 10.47 13.35 10.52 13.30 1 10.58 i 13.26 10.64 17 18 14.18 11.08 14.14 11.14| 14.09 I 11.21 i! 14.04 11.27 18 19 14.97 11.70 14.92 11.76 ; 14.87' 11.83 ;| 14.82 11.89 19 20 21 15.76 12.31! 15.71 12.38 i! 15.65 ; 12.45 !i 15.60 12.52 20 16.55 12.93 16.49 i 13.00 16.43 13.07 ' 16.38 13.14 21 22 17.34 13.54 17.28 13.62 17.22 ; 13.70 li 17.16 13.77 22 23 18. U 14.16 18.06 14.24 18.00 i 14.32 i 17.94 14.40 23 24 18.91 14.78; 18.85 14.86 i 18.78 ! 14.94 ' 18.72 15.02 24 25 19.70 15.39 19.63 15.481 19.. 57 15.56 i 19.50 15.65 25 2fi 20.49 16.01 20.42 16.10 20.35 16.19 i 20.28 16.27 26 27 21.28 16.62 21.20 16.72 21.13 16.81 1 21.06 16.90 27 28 22.06 17.24 21.99 17.33 21.91 17.43 21.84 17.53 28 29 22.85 17. S5 22.77 17.95 22 . 70 18.05' 22.62 18.15 29 30 1 23.64 18.47 i 23.56 18.57 23.48 18.68 23.40 24.18 18.78 30 31 24.43 19.09 24.34 19.19 24.26 19.30 19.40 31 32 25.22 19.70 25.13 ! 19.81 25.04 1 19.92 24.96 20.03 32 33 26.00 20.32 25.92 i 20.43 25.83 120.54 25.74 20.66 33 34 26.79 20.93 26.70 i 21.05 26.61 1 21.17 26.52 21.28 34 35 27.58 21.55 27.49 121.67 27.39 1 21.79 i 27.30 21.91 35 36 28.37 22.16 28.27 122.29 28.17 1 22.41 ■' 28.08 22.53 36 37 29.16 22.78 29.06 i 22.91 28.96 23.03 i 28.86 23.16 37 38 29.94 23.40 29.84 123.53 29.74 23.66 ; 29.64 23.79 38 39 30.73 24.01 30.63 i 24.14 .30.52 24.28 ; 30.42 124.41 39 40 31.52 24.63 25.24 31.41 124.76 31.30 24.90 25.52 31.20 [25.04 40 41 32.31 32.20: 25.38 32.09 31.98 25.66 41 42 33.10 25.86 32 . 98 i 26 . 00 32.87 1 26.15; 32.76 26.29 42 43 33.88 26.47 33.77 26.62 33.65 1 26.77 33.53 126.91 43 44 34.67 27.09 34.. 55 27.24 34.43: 27.39 i 34.31 127.54 44 45 35.46 27.70 35.34 27.86 35.22; 28.01 ' 35.09 128.17 45 46 36.25 28.32 36.12 28.48 36.00 28.64 i 35.87 128.79 46 47 37.04 28.94 36.91 29.10 36.78 29.26 36.65 29.42 47 48 37.82 29.55 37.70 29.72 37.57 29.88 37.43 30.04 48 49 38.61 30.17 38.48 30.34 38.35 30. .50 38.21 30.67 49 50 39.40 30.78 39.27 30.95 39.13 31.13 i:38. 99 31.30 50 o a .2 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 1 5^> Deg 511 Deg. 5U Deg. ' 5U Deg. TRAVERSE TABLE. 79 o 5' S P 51 38 Deg. 38i Deg. 38^ Deg- 381 Deg. 9 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 40.19 31.40 40.05 31.57 39.91 31.75 39.77 31.92 51 52 40.98 32.01 40.84 32.19 40.70 32.37 40.55 32.55 52 53 41.76 32.63 41.62 32.81 41.48 32.99 41.33 33.17 53 54 42.55 33.25 42.41 33.43 42.26 33.62 42.11 33.80 54 55 43.34 33.86 43.19 34.05 43.04 34.24 42.89 34.43 55 56 44.13 34.48 43.98 34.67 43.83 34.86 43.67 35.05 56 57 44.92 35.09 44.76 35.29 44.61 35.48 44.45 35.68 57 58 45.70 35.71 45.55 35.91 45.39 36.11 45.23 36.30 58 59 46.49 36.32 46.33 36.53 46.17 36.73 46.01 36.93 59 60 61 47.28 36.94 47.12 37.15 46.96 37.35 46.79 37.56 60 48.07 37.56 47.90 37.76 47.74 37.97 47.57 38.18 61 62 48.86 38.17 48.69 38.38 48.52 38.60 48.35 38.81 62 63 49.64 38.79 49,47 39.00 49.. 30 39.22 49.13 39.43 63 64 50.43 39.40 50.26 39.62 50.09 39.84 49.91 40.06 64 65 51.22 40.02 51.05 40.24 50.87 40.46 50.69 40.68 65 66 52.01 40.63 51.83 40.86 51.65 41.09 51.47 41.31 66 67 52.80 41.25 52.62 41.48 52.43 41.71 52.25 41.94 67 68 53.58 41.86 53.40 42.10 53.22 42.33 53.03 42.56 68 69 54.37 42.48 54.19 42.72 54.00 42.95 53.81 43.19, 691 70 71 55.16 43.10 54.97 43.34 54.78 43.58 54.59 43.81 70 55.95 43.71 55.76 43.96 55.57 44.20 55.37 44.44 71 72 56.74 44.33 56.54 44.57 56.35 44.82 56.15 45.07 72 73 57.52 44.94 57.33 45.19 57.13 45.44 56.93 45.69 73 74 58.31 45.56 58.11 45.81 57.91 46.07 67.71 46.32 74 75 59.10 46.17 58.90 46.43 58.70 46.69 58.49 46.94 75 76 59.89 46.79 59.68 47.05 59.48 47.31 59.27 47.57 76 77 60.68 47.41 60.47 47.67 60.26 47.93 60.05 48.20 77 78 61.46 48.02 61.25 48.29 1 61.04 48.56 60.83 48.82 78 79 62.25 48.64 62.04 48.91 i 61.83 49.18 61.61 49.45 79 80 81 63.04 49.25 62.83 49.53! 62.61 49.80 62.39 50.07 80 63.83 49.87 63.61 50.15 163.39 50.42 63.17 50.70 81 82 64.62 50.48 64.40 50.77 1 64.17 51.05 63.95 51.33 82 83 65.40 51.10 65.18 51.38: 64.96 51.67 64.73 51.95 83 84 66.19 51.72 65.97 52.00' 65.74 52.29 65.51 52.58 84 85 66.98 52.33 66.75 52.62:166.52 52.91 66.29 53.20 85 86 67.77 52.95 67.54 53.^24 167.30 53.54 67.07 53.83 86 87 68.56 53.56 68.32 53.86 '68.09 54.16 67.85 54.46 87 88 69.34 54.18 69.11 54.48 : 68.87 54.78 68.63 55.08 88 89 70.13 54.79 69.89 55.10 169.65 55.40 69.41 55.71 89 90 91 70.92 55.41 70.68 .55.72 70.43 56.03 70.19 56.33 56.96 90 91 71.71 56.03 71.46 56.34 71.22 56.65 70.97 92 72.50 56.64 72.25 56.96 72.00 57.27 71.75 57.58 92 93 73,28 57.26 73.03 57.58 .72.78 57.89 72.53 58.21 93 94 74.07 57.87 73.82 58.19 ;i 73.57 58.52 73.31 58.84 94 95 74.86 58.49 74.61 58.81 174.35 59.14 74.09 59.46 95 96 75.65 59.10 75.39 59.43 75.13 59.76 74.87 60.09 96 97 76.44 59.72 76.18 60.05 '75.91 60.33 75.65 60.71 97 98 77.22 60.33 76.96 60.67 76.70 61.01 76.43 61.34 98 99 78.01 60.95 77.75 61.29/77.48 61.63 77.21 61.97 99 100 6 o .2 Q 78.80 61.57 78.53 61.91 ! 78.26 62.25 77.99 62.. 59 100 Dep. Lat. Dep. Lat. I Dep. Lat. Dep. Lat. 1 5 52 Deg. 511 Deg. 5U Deg. SU Deg. 80 TEAVERSE TABLE. 5 an » CD ~1 39 Deg. 39i Deg. 39i Deg. 391 Deg. 1 1 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0.78 0.63 0.77 0.63 j 0.77 0.64 0.77 0.64 2 1.55 1.26 1.55 1.27 1 1.54 1.27 1.64 1.28 2 3 2.33 1.89 2.32 1.90 ll 2.31 1.91 2.31 1.92 3 4 3.11 2.52 3.10 2.53 1 3.09 I 3.86 2.64 3.08 2.56 4 5 3.89 3.15 3.87 3.16 3.18 3.84 3.20 6 6 4.66 3.78 4.65 3.80 1 4.63 3.82 4.61 3.84 6 7 5.44 4.41 5.42 4.43 5.40 4.45 6.38 4.48 7 8 6.22 5.03 6.20 5.06 |l 6.17 5.09 6.15 6.12 8 9 6.99 , 5.66 6.97 5.69 ll 6.94 5.72 6.92 6.75 9 10 11 7.77 6.29 7.74 6.33 1! ^-72 6.36 7.69 6.39 10 11 8.65 6.92 8.52 6.96 8.49 7.00 8.46 7.03 12 9.33. 7.55 9.29 7.59 9.26 7.63 9.23 7.67 12 13 10.10 8.18 10.07 8.23 10.03 8.27 9.99 8.31 13 14 10.88 ; 8.81 10.84 8.86 10.80 8.91 10.76 8.95 14 15 11.66 9.44 11.62 9.49 11.57 9.54 11.53 9.69 16 16 12.43 10.07 12.39 10.12 12.35 10.18 12.30 10.23 16 17 13.21 10.70 13.16 10.76 13.12 10.81 13.07 10.87 17 18 13.99 11.33 13.94 11. .39 13.89 11.45 13.84 11.51 18 19 14.77 11.96 14.71 12.02 14.66 12.09 14.61 12.15 19 20 21 15.54 12.59 15.49 12.65 [ 15.43 12.72 15.38 12.79 20 21 16.32 13.22 16.26 13.29 ' 16.20 13.36 16.15 13.43 22 17.10 ! 13.84 17.04 13.92 16.98 13.99 16.91 14.07 22 23 17.87 14.47 17.81 14.55 17.75 14.63 17.68 14.71 23 24 18.65 15.10 18.59 15.18 18.52 15.27 18.45 15.35 24 25 19.43 , 15.73 19.36 15.82 19.29 15.90 19.22 15.99 25 26 20.21 i 16.36 20.13 16.45 20.06 16.54 17.17 19.99 16.63 26 27 20.98 1 16.99 20.91 17.08, 20.83 20.76 17.26 27 28 21.76 i 17.62 21.68 17.72 21.61 17.81 21.53 17.90 28 29 22.54 ■ 18.25 22.46 18.35 22.38 18.45 22,30 18.54 29 30 31 23.31 ; 18.88 24.09 1 19.51 23.23 18.98 23.15 19.08 23.07 19.18 30 24.01 19.61 23.92 19.72 23.83 19.82 31 32 24.87,20.14 24.78 20.25 24.69 20.35 24.60 20.46 32 33 25.65 20.77 25.55 20.88 25.46 20.99 25.37 21.10 33 34 26.42 121.40 26.33 21.51 26.24 21.63 26.14 21.74 34 35 27.20 22.03 27.10 22.14 27.01 22.26 26.91 22.38 35 36 27.98 22.66 27.88 22.78 27.78 22.90 27.68 23.02 36 37 28.75 23.28 28.65 23.41 28.55 23.53 28.45 23.66 37 38 29.53 23.91 29.43 24.04 29.32 24.17 29.22 24.30 38 39 30.31 24.54 30.20 24.68 30.09 24.81 29.98 24.94 39 40 41 31.09 25.17 30.98 25.31 30.86 25.44 30.75 25.58 40 41 31.86 25.80 31.75 25.94 31.64 26.08 31.52 26.22 42 32.64 26.43 32.52 26.57 32.41 26.72 32.29 26.86 42 43 33.42 27.06 33.30 27.21 33.18 27.36 33.06 27.50 43 44 34.19 27.69 34.07 27.84 33.95 27.99 •33.83 28.14 44 45 34.97 28.32 34.85 28.47 34.72 28.62 34.60 28.77 45 46 35.75 28.95 35.62 29.10 36.49 29.26 35.37 29.41 48 47 36.53 29.58 36.40 29.74 36.27 29.90 36.14 30.05 47 48 37.30 30.21 37.17 30.37 37.04 30.53 36.90 30.69 48 49 38.08 30.84 37.95 31.00 37.81 31.17 37.67 31.33 49 _50 6 i to O 38.86 31.47 j 38.72 31.64 38.58 31.80 38.44 31.97 50 Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 51 Deg. 1 50| Deg. 50^ Deg. 50i Deg. s CO TRAVERSE TABLE. 81 9 51 39 Deg. 39i Deg. m Deg. 391 Deg. o CD ~5l Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 39.63 32.10 39.49 32.27 39.35 32.44 39.21 32.61 52 40.41 32.72 40.27 32.90 40.12 33.08 39.98 33.26 52 53 41.19 33.35 41.04 33.53 40.90 33.71 40.76 33.89 53 54 41.97 33.98 41.82 34.17 41.67 34.35 41.52 34.53 54 55 43.74 34.61 42.59 34.80 42.44 34.98 42.29 35.17 55 56 43.52 35.24 43.37 35.43 43.21 35.62 43.06 35.81 56 57 44.30 35.87 44.14 36.06 43.98 36.26 43.82 36.45 57 58 45.07 36.50 44.91 36.70 44.75 36.89 44.59 37.09 58 69 45.85 37.13 45.69 37.33 45.53 37.53 45.36 37.73 59 60 61 46.63 37.76 46.46 37.96 46.30 38.16 46.13 38.37 60 61 47.41 38.39 47.24 38.60 47.07 38.80 46.90 39.01 62 48.18 39.02 48.01 39.23 47.84 39.44 47.67 39.65 62 63 48.96 39.65 48.79 39.86 48.61 40.07 48.44 40.28 63 64 49.74 40.28 ! 49.56 40.49 49.38 40.71 49.21 40.92 64 65 50.51 40.91 50.34 41.13 ,50.16 41.35 49.97 41.56 65 66 51.29 41.54! 51.11 41.76 50.93 41.98 50.74 42.20 66 67 52.07 42.16 ' 51.88 42.39 51.70 42.62 51.51 42.84 67 68 52.85 42.79 ' 52.66 43.02 52.47 43.25 52.28 43.48 68 69 53.52 43.42 1 53.43 43.66 53.24 43.89 53.05 44.12 69 70 71 54.40 44.05 1 54.21 54.98 44.29 54.01 44.53 53.82 44.76 45.40 70 71 55.18 44.68 1 44.92 54.79 45.16 54.59 72 55.95 45.31 1 55.76 45.55 55.56 45.80 55.36 46.04 72 73 56.73 45.94 1 56.53 46.19 56.33 46.43 56.13 46.68 73 74 57.51 46.57 57.31 46.82 57.10 47.07 56.89 47.32 74 75 58.29 47.20 58.08 47.45 57.87 47.71 '57.66 47.96 75 76 59.06 47.83 58.85 48.09 58.64 48.34 1.58.43 48.60 76 77 59.84 48.46 59.63 48.72 59.42 48.98 '59.20 49.24 77 78 60.62 49.09 60.40 49.35 60.19 49.61 i .59.97 49.88 78 79 61.39 49. T2 61.18 49.98 60.96 .50.25 160.74 50.52 79 80 81 62.17 50.. 35 61.95 50.62 61.73 .50.89 ;61.51 51.16 80 81 62.95 50.97 62.73 51.25 62.50 51.52 ] 62.28 51.79 82 63.73 51.60 63.50 51.88 63.27 52.16 63.04 52.43 82 83 64.50. 52.23 64.27 52.51 64.04 .^)2.79 163.81 53.07 83 84 65.28 52.86 65.05 53.15 64.82 53.43 ! 64.58 53.71 84 85 66.06 53.49 65.82 53.78 65.59 54.07 65.35 54.35 85 86 66.83 54.12 66.60 54.41 66.36 54.70 166.12 54.99 86 87 67.61 54.75 67.37 55.05 67.13 55.34 : 66.89 55 . 63 87 88 68.39 55.38 68.15 55.68 67.90 55.97 67.66 56.27 88 89 69.17 56.01 68.92 56.. 32 68.67 56.61 i 68.43 56.91 89 90 91 69.94 56.64 69.70 56.94 69.45 .57.25 169.20 57.55 90 91 70.72 57.27 70.47 57.58 70.22 57.88 ,69.96 58.19 92 71.50 57.90 71.24 58.21 70.99 58.52 70.73 58.83 92 93 72.27 58.53 72.02 58.84 71.76 59.16 1 71.50 ,59.47 93 94 73.05 59.16 72.79 59.47 72.53 59.79 172.27 60.11 94 95 73.83 59.79 73.57 60.11 73.30 60.43 73.04 60.75 95 96 74.61 60.41 74.34 60.74 74.08 61.06 73.81 61.39 90 97 75.38 61.04 75.12 61.37 74.85 61.70 74.58 62.03 97 98 76.16 61.67 75.89 62.01 75.62 62.34 75.35 62.66 98 99 76.94 62.30 76.66 62.64 76.39 62.97 76.12 63.30 99 100 6 o a 1 77.71 62.93 77.44 63.27 77.16 63.61 76.88 63.94 100 Q Dep. ■ Lat. Dep. Lat. Dep. Lat. Dep. Lat. 51 Deg. 501 Deg. 50i Deg. 50\ Deg. 82 TRAVEESE TABLE. ^— — • — ^ ■— .^ — — — 1 ■^ C 1 40 Deg. : 40i I>&g. \ 40^ Deg. m Deg. C 1 Lat. ll 0.77 Dep. \ Lat. 0.64 0.76 Dep. ;; Lat. 0.65 ; 0.76 Dep. 0.65 1 Lat. 0.76 iDep. 0.65' ll 2 1.53- 1.29 1.53 1.29 i! 1.52 1.30 1..52 1.31 2 3| 2.30 1.93 2.29 1.94 1; 2.28 1.95 2.27 1.96 3 4< 3.06 2.57 3.05 2.58 1 3.04 2.60 3.03 2.61 4 5| 3. S3 3.21 i 3.82 3.23 ;. 3.80 3.25 3.79 3.26 5 6 4.60 3.86;! 4.58 3.88 i: 4. .56 3.90 4.55 3 . 92 6 7 5.36 4.50 5.34 4.52 'v 5.32; 4.55 5 . 30 4.57 7 8 6.13 5.14 6.11 5.17 |i 6.08 : 5.20 fi .("16 5 . 22 8 9i 6.89 5.79] 6.87 5.82 ii 6.84: 5.84 6.S2 5.87 9 10 i 7.66 11 : 8.4:3 6.43 I 7.63 7.07 1 8.40 6.46 1; 7.60 6.49 7.14 7.58 8 . 33 6.53 7.18 10 n 7.11 ii 8.36 12' 9.19 7.71 1 9.16 7.75 ij 9.12; 7.79 9.09 7.83 12 13. 9.96 8.36 ! 9.92 8.40 il 9.89 8.44 9.85 8.49 13 14 10.72 9.00 1 10.69 9.05 l':^,^? 9.09 10.61 9.14 U 1.5 il.49 9.64 ! 11.45 9.69 :: .: 9.74 11.36 9.79 15 16 12.26 10.28 1 12.21 10.34 .: :: 10.39 12. '12 10.44 16 17 13.02 10.93 12.97 10.98 , 12.93 11.04 12.88 n.io 17 ' IS 13.79 11.57 ' 13.74 11.63,13.69 11.69 13.64 11.75 18 19 14.55 12.21 : 14.50 12.28 : 14.45 12.34 14.39 12.40 19 20 15.. 32 12.86 i 15.26 12.92 15.21 12.99 15.15 13.06 20 21 16.09 13. .50 • 16.03 13.57 15.97 13.64 15.91 13.71 21 22 16.85 14.14; 16.79 14.21 16.73 14.29 16.67 U.36 22 23 17.62 14.78 17.55 14.86 -7^^ 14.94 17.42 15.01 23 24 18,39 15.43 18.32 15.51 1^.2c 15.59 18.18 15.67 24 25 19.15 16.07 19.08 16.15 19.01 1 16.24 18.94 16.32 25 26 19.92 16.71 19.84 16. SO : 19.77 ! 16.89 19. 7y 16.97 26 27 20.68 17.36 20.61 ; 17.45 ^ 20.53 17. .54 20 . i5 17.62 ■^7 2S 21.45 18.00, 21.37 i 18.09 21.29 18.18 21.21 IS. 2^ 28 29 22.22 1S.64 22.13; 18.74 22.05 18.83 21.97 18.93 29 -30 22.98 19.28 22.90 19.38 22.81 19.48 J2.73 23.48 19. 5S 20.24 30 31 31 23.75 19.93 23.66 20.03 23.57 20.13 32 24.51 20.57 24.42 20.68 24.33 20.78 24.24 20. S 9 32 33 : 25.2? 21.21 25. ly 21.32 25.09 21.4? 25.00 21.54 33 :34 26.05 21. S5 25-95 21.97 25.85 22.08 25.76 22. 19 34 35 26. SI 22.50 2-. 71 22.61 26.61 22.73 26.51 22 . S5 35 36 27. 5S 23. U 27^- 23.25 27.37 23.38 27.27 33.50 36 37 2S.34 23, 7S u-,;^ 23. 9 i 2S.13 24.03 28.03 24.15 37 3- 2y.:i 21,43 29,'." 24.55 2S.90 24.68 28.79 24.80 3S 39 2H.Si 25,-7 2y,77 25.20 29.66 25 . 33 29.54 25.46 39 40 3u . 64 25 . 7 i 30 . 53 25 . S4 30 . 43 25.98 30 . 30 26.11 40 41 31.41 26.35 31.29 26.49 31 . 18 26. e3 31.06 2G.76 41 42 32.17 27.00 32.06 27.14 31.94 27.28 31.82 27.42 42 43 32.94 27,64 32.82 .27.78 32.70 27.93 32.58 28.07 43 44 33.71 2S.2S 33.58 28.43 33.46 28.. 58 33.33 28.72 44 45 31.47 2S.93 34.35 29.08 34.22 29.28 34.09 29.37 45 . 46 35.24 29.57 35.1] 29.72 34.98 29.87 34.85 30.03 46 47 36.00 30.21 35. S 7 30.37 35.74 30 . 52 35.61 30.68 47 48 36.77 30.85 . 36.64 31.01 36.50 31.17 36.36 31.33 48 49 37.54 31.50 , 37.40 31.66 37.26 31.S2 37.12 31.99 49 .50 3S.30 32.14 38.16 .32.31 : 38.02 Dep. j Lat. |: Dep. 32.47 Lat. 37.88 32.64. 50 i Dep. Lat. Dep. 1 Lat. 1 S 1 =: C [1 /'^ \ 50 Deff. u 49| Deg. 1 49^ Deg, i " i! i : 49i Deg. !5 fRAVfiRSE TABLE. 83 m P S n o 40 Deg. 40i Deg. 40^ Deg. 401 Deg. 1 s ? '51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 39.07 32.78 1 38 . 92 32.95 38 . 73 33.12 38.64 33.29 52 39.83 33.42 ! 39.69 33.60 39.. 54 33.77 .39.39 33.94 52 53 40.60 .34.07 i 40.45 34.^4 40.30 34.42 40.15 34.60 53 54 41.37 34.71 41.21 34.89 41.06 35.07 40.91 35.25 54 55 42.13 .35.35 1 41.98 35.54 41.82 35.72 41.67 35.90 55 56 42.90 36.00 42.74 36.18 42.58 .36.37 42.42 36.55 56 57 43.66 36.64 43.50 36.83 43.34 37.02 43.18 37.21 57 58 44.43 37.28 44.27 37.48 44.10 37.67 43.94 37.86 58 59 45.20 37.92 45.03 3S.12 44.86 .38.32 44.70 38.51 59 60 61 45.96 38.57 45.79 38.77 45.62 38.97 39.62 45.45 39.17 60 48.73 39.21 46 . 56 39.41 46.38 46.21 39.82 61 62 47.49 39.85 47.32 40.06 47.15 40.27 46.97 40.47 62 63 48.26 40.50 48.08 40.71 47.91 40.92 47.73 41.12 63 64 49.03 41.14 48.85 41.35 48.67 41..56j{ 48.48 41.78 64 65 49.79 41.78 49.61 42.00 49.43 42.21 1149.24 42.43 65 66 50.56 42.42 50.37 42.64 60.19 42.86 II 50.00 43.08 66 67 51.32 43.07 51.14 43.29 50.95 43.51 50.76 43.73 67 6S 52.09 43.71 51.90 43.94 51.71 44.16 51.51 44.39 68 69 52.86 44.35 52.66 44.58 52.47 44.81 .52.27 45.04 69 70 71 ,53.62 45.00 53.43 45.23 53.23 45.46 i 53.03 45.69 70 71 54.39 45.64 54.19 45.87 53,99 46.11 1153.79 46., 35 72 55.16 46.28 .54.95 46.52 54.75 46.76 li 54.54 47.00 72 73 55.92 46.92 55.72 47.17 55.51 47.41 1155.30 47.65 73 74 56.69 47.. 57 56.48 47.81 56.27 48.06 56.06 48.30 74 75 57.45 48.21 57.24 48.46 57.03 48.71 .56.82 48.96 75 76 .58.22 48.85 58.01 49.11 57.79 49.36 ,57.57 49.61 76 77 58.99 49.49 58.77 49.75 58., 55 50.01 ,58.33 50.26 77 78 59.75 50.14 59.53 .50.40 59.31 50.66 59.09 50.92 78 79 60.. 52 50.78 60.30 51.04 60.07 51.31 59.85 51.57 79 80 8i 61.28 51.42 61.06 61.82 51.69 60.83 51.96 52.61 60.61 52.22 80 81 62.05 52.07 52.34 61.59 61.36 52.87 82 62.82 52.71 62.59 52.98 62.35 53.25 62.12 53.53 82 83 63.. 58 53.35 63.35 53.63 63.11 .53.90 62.88 54.18 83 84 64.35 53.99 64.11 54.27 63.87 54.55 63.64 54.83 84 85 65.11 54.64 64.87 54.92 64.63 55.20 64.39 .55.48 85 86 65.88 55.28 65.64 55.57 65.39 55.85 65.15 56.14 86 87 66.65 55.92 66.40 56.21 66.16 56.50 65.91 56.79 87 88 67.41 56.57 67.16 56.86 66.92 57.15 66.67 57.44 88 89 68.18 57.21 67.93 57.50 67.68 57.80 67.42 58.10 89 90 91 68.94 57.85 68.69 58.15 68.44 58.45 68.18 58.75 90. 69.71 58.49 69.45 58.80 69.20 59.10 68.94 59.40 91. 92 70.48 59.14 70.22 59.44 69.96 59.75 69.70 60.05 95 93 71.24 59.78 70.98 60.09 70.72 60.40 70.45 60.71 9n 94 72.01 60.42 71.74 60.74 71.48 61.05 71.21 61.36 94 95 72.77 61,06 72.51 61.38 72.24 61.70 71.97 62.01 95 96 73.54 61.71 73.27 62.03 73.00 62.35 72.73 62.66 96 97 74.31 62.35 74.03 62.67 73.76 63.00 73.48 63.32 97 98 75.07 62.99 74.80 63.32 74.52 63.65 74.24 63.97 98 99 75.84 63.64 75.56 63.97 75.28 64.30 75.00 64.62 99 100 76.60 64.28 76.32 Dep. 64.61 76.04 64.94 75.76 65.28 100 Dep. Lat. Lat. Dep. Lat. Dep. Lat. ?. ' 1 O 50 Deg. 49J Deg. 49^ Deg. 49i Deg. .28 64 TfiAVERSZ TABLE. 41 Deg. 41ir Des. 4U Dez. 4 Deg. Lat. { Dep. La:, ^ Dep. Lat, 8 9 10 0.75 1.51 2.26 3.02 3.77 4.. 53 5.2S 6.04 6.79 7.55 0.66 ].31 1.97 2.62 3.28 3.94 4.59 5.25 5.90 6.56 lO ..50 1.26 0.66 1.32 1.93 8.30 9.06 9.81 10.. 57 11.32 16 i 12.08 17 i 12.83 18 13.58 19 i 14.34 20' 15.09 11 i 12 13 14 15 7.87 8.53 9.1? 9.84 10.50 11.15 11.81 12.47 13.12 21 I 15.85 22 16.60 23 17.36 24 25 26 27 28 29 30 31 34 35 18.11 18.87 19.62 20.38 21.13 21.89 22.64 13.78 14.43 15.09 15.75 16.40 17.06 17.71 18.37 19.03 19.68 23.40 24.15 24.91 25.66 26.41 27.17 27.92 28.68 29.43 30.19 37 I 38! 39 40| 41 130.94 42 [31.70 43 I 32.45 44I33.2I 45; 33.96 46 '34.72 47 i 35.47 20.34 20.99 21.65 22.31 22 . 96 23.62 24.27 24.93 25.. 59 26.24 26.90 3.01 2.64: 3.78 3.30 4.51 3.96 5.26 4.62 6.01 5.27 6.77 5.93; 7.52 6.59 S 97 - .- r 0.75 1.50 2.25 3.00 3.74 4.49 5.24 5.99 6.74 -.49 Dep. 0.66 1.33 1.99 2.65 3.31 3.98 4.64 5.30 5.96 6.63 Lat Dep. 0.75 i 1.49 i 2.24 i 2.98 3.73 4.48 5,22 : '5.97 j 6.71; 7.46 0.67 1..33 2.00 2.66 3.33 4.00 4.66 5.-33 5.99 12.03 i 12.78 13.53' 14. 2S 15.04 - .- r ^.■:4 7.29 1 7 0' ^.yy 7.95! V ' ^ 9.74 8.61 - , ■; .- 10.49 9.28 1 i? . 5i? 11.23 9.94i 10.. 55 11.98 10.60 11.21 12.73 11.26 11.87 13.48 11.93, 12.53 14.23 12.59! 13.19 14.93 13.25 1 15.79 [ 16.54; 17.29^ 18.04! 18.80! 19.55; 20.30, 21.05 ( 21.80' 22.56^ 23.?; 24.0- 24. SI 25.56 26.31 13.85 14.51 15.16 15.S2 16.48 17.14 17.80 18.46 19.12! 19.78 ', i . i o 22.42 23.08 48 49 50 36.23 36.98 37.74 27 55 28 21 28 87 29 52 30 18 30.83 31 49 . 32 15' 28 . 5 7 29.32 30.07 30. V? 31 r- 32. SI 33. 0^ 33. Si 34.0- 35.?^ 36 . '. r 36. i4 25.71 26 . 37 32.80 s: 8.21 8.95 9.70 10.44 11.19 11.94 12.68 13.43 14.18 14.92 15.73 16.48 ; 17.23 ! 17.97! 18.72 19.47 20.22 20.97 21.72 22.47 23 . 22 23.97 24.72 25.46 26.21 26.96 27.71 28.46 29.21 29 . 96 13.91 14.58 15.24 5.90 16.57 17.23 17.89 18.. 55 19.22 19.88 15.67 I 16.41 ! 17.16 I 17.91 18.65 I 19.40 20.14 20.89 21.64 22.38 6.66 I JO 11 12 13 14 15 16 17 18 19 JO 21 22 •23 24 25 26 7.32 7.99 8.66 9.32 9.99 10.65 11.32 11.99 12.65 13.32 23.13 23.87 24.62 25.37 26.11 26.85 52 1127.60 18!' 28.35 84'! 29.10 50 ; 29.84 13.98 14.65 15.32 15.98 16.65 17.31 17.98 18.64 19.31 19.98 20.64 I 21.31 21.97 22.64 23.31 23.97 24.64 25.30 25.97 26.64 30.71 !27 31.46 32.21 32.95 33 . 70 34.45 35 . 20 35 . 95 36.70 37.45 17 [ 30.59 83 31.33 49 i! 32.08 16 I 32.83 33.-57 34.32 35.06 35.81 36.. 56 37.30 27.30 27.97 28.63 29.30 29.97 30.63 31.30 31.96 32.63 33.29 28 29 _?? 31 .32 33 34 35 If 38 39 _40 41 42 43 44 45 46 47 48 49 .50 S I Dep. j Lat, ^ Dep. j Lat. Dep. Lat. '<\ Dep. ■ Lat. 49Deff. 4Si Der. 4St Deg. 4Si Deg. TBAVERSE TABLE. 85 5 P 1 51 41 Deg. 4U Deg. 41 i Deg. 411 Deg. 9. 1 51 Lat. Dep. Lat. 1 Dep. Lat. Dep. Lat. Dep. 38.49 33.46 i 38.34 1 33.63 38.20 33.79 38.05 33.96 52 39.24 34.12 1 39 -.10 1 34.29 38.95 34.46 .38.79 34.63 52 53 40.00 34.77 39.85 34.95 39.69 35.12 39.54 35.29 53 54 40.75 35.43 1 40.60 ' 35.60 40.44 35.78 40.29 35.96 54 55 41.51 36.08 1 41.35 ! 36.26 41.19 33.4^1: 41.03 36.62 55 56 42.26 36.74 ii 42.10 1 36.92 41.94 37.11 41.78 37.29 56 57 43.02 37.40 1' 42.85 1 37.58 42.69 37.77! 42.53 37.96 57 58 43.77 38.05 1 43.81 i 38.24 43.44 38.43 1 43.27 38.62 58 59 44.53 38.71 1 44.36:38.90 4-4.19 39.09 1 44.02 39.29 59 60 61 45.28 46.04 1 39.36 i 45.11 1 39.56 1 44.94 39.76 II 44.76 39.95 60 61 40.02 : 145.86 \ 40.23 i 45.69 1 40.42 |j 45.51 40.62 62 46.79 40.68; 46.61 ; 40.88 46.44! 41.08 46.26 41.28 62 63 47.55 41.33^ 47.37:41.-54 47.18 ; 41.75 47,00 41.95 63 64 48.30 41.99: 48.12 ! 42.20 47.93 142.41 47.75 42.62 64 65 49.06 42.641 48.87 142.86 48.68 1 43.07 48.49 43.28 65 66 49.81 43.30 ! 49.62 43.52 49.43 143.73 49.24 43.95 66 67 50.57 43.96 i| 50.37 1 44. 18 50.18 1 44.40 1 49.99 44.61 67 68 51.32 44.611 51.13 44.84 50.93 1 45.06 | 50.73 45.28 68 69 52.07 1 45.27 !| 51.88 ^ 45.49 ! 51.68 45.72 1 51.48 45.95 69 70 71 52.83 45.92' 52.63 146.] 5 .52.43 46.38 1 47.05 1 52.22 46.61 70 53.58 46.. 5S 1 53.33 '46. Si 53. iS .52.97 147.28 71 72 54.34 47.24 i' 54. 13 47.47 53.92 147.71 53.72 j 47.94 72 73 55.09 47.89! 54.88 48..55:' 55.64 48.13 .54.67 48.37 54.48 148.61 73 74 55.85 48.79 .55.42 ,49.03 55.21 49.28 74 75 56.60 49.20; .56.39 49.45 66.17 49.70 55.95 49.94 75 76 57.36 49.86 1 57.14 50.11 56.92 1 50.36 56.70 50.61 76 77 58.11 50.52 57.89 .50.77 57.67 151.02 57.45 51.27 77 78 58.87 51.17 68.64 51.43 .58.42 51.68 58.19 51.94 78 79 59.62 51.83 59.40 52.09 59.17 52.35 58.94 52.60 79 80 81 60.38 52.48 53.14 60.15 52.75 .59.92 53.01 59.68 53.27 80 61.13 60.90 53.41 60.67; 53.67 60.43 53.94 81 82 61.89 53.80 61.65 54.07 61.41 54.33 61.18 54.60 82 83 62.64 54.45 62.40 .54.73 62.16 55.00 61.92 ,55.27 83 84 63.40 55.11 63.15 55.38 62.91 55.66 62.67 55.93 84 85 64.15 55.76 63.91 56.04 63.66 56.32 63.41 56.60 85 86 64.90 56.42 64.66 56.70 64.41 56.99 64.16 57.27 86 87 65.66 57.08 65.41 57.36 65.16 57.65 64.91 57.93 87 88 66.41 57.73 66.16 58.02 65.91 58.31 65.65 58.60 88 89 67.17 58.39 66. 9i 58.68 66.66 58.97 66.40 59.26 89 90 91 67.92 68.68 1 59.05 1.59.70 67.67 59.34 67.41 59.64 67.15 59.93 90 68.42 60.00 68.15 60.30 67.89 60.60 91 92 69.43 60.36 69.17 60.66 68.90 60.96 68.64 61.26 92 93 70.19 161.01 69.92 61.32 69.65 61.62 69.38 61.93 93 94 70.94 61.67 70.67 61.98 70.40 62.29 70.13 62.59 94 95 71.70 62.33 71.43 62.64 71.15 62.95 70.88 63.20 95 96 72.45 62.98 72.18 63.30 71.90 63.61 71.62 63.92 96 97 73.21 63.64 72-93 63.96 72.65 64.27 72.37 64.59 97 98 73.96 64.29 73.68 64.62 73.40 64.94 73.11 65.26 98 99 74.72 i 64.95 74.43 65.28 74.15 65.60 73.86 65.92 99 100 a .2 75.47 65.61 75.18 65.93 74.90 66.26 74.61 66.. 59 100 ai o a i p Dep. Lat. Dep. Lat. Dep Lat. Dep. Lat. 49 Deg. 481 Deg. 1 48^ Deg. 48i Deg. SB TB AVERSE TABLE. 5" 42 Deg. 1 42i Deg. 1 42i Deg. 421 Deg. 3 1 r Lat. j Dep. Lat. Dep. Lat. 1 Dep. I Lai. Dep. 1 0.74 0.67 0.74 0.67 1 0.74 0.68 || 0.73 1.35 1 1.47 2.03' 2.20 0.68 2 1.49 1.34 1.48 1.34 1 1.47 1.36 2 3 2.23 2.01 2.22 2.02 ! 2.21 2.04 3 4 2.97 2.68 2.96 2.69 2.95 2.70 1 2.94 2.72 4 5 3.72 3.35 3.70 3.36 3.69 3.38 ii 3.67 3.39 5 6 4.46 4.01 4.44 4.03 4.42 4.05 1! 4.41 4.07 fi 7 1 5.20 4.68 ! 5.18 4.71 1 5.16 4.73 1 5.14 4.75 7 8 5.95 5.35 ! 5.92 5.38 j 5.90 5.40: 5.87 5.43 8 9 6.69 6.02 1 6.66 6.05 6.64 6.08: 6.61 6.11 9 10 7.43 6.69 1 7.40 6.72 7.37 6.76: 7.,S4 6.79 10 11 8.17 7.36 ' 8.14 7.40 8.11 7.43 8.08 7.47 n 12 8.92 8.03 ' 8,88 8.07 8.85 8.11 1 8.81 8.15 12 13 9.66 8.70 9.62 8.74 9.58 8.78 : 9.55 8.82 13 14 10.40 9.37 10.36 9.41 10.32 9.46 10.28 9.50 14 15 11.15 10.04 11.10 10.09 11.06 10.13 11.01 10.18 15 16 1 11.89 10.71 11.84 10.76 11.80 10.81 11.75 10.86 16 17 12.63 11.38 12.58 11.43 ' 12.53 11.48 12.48 11.54 17 18 13.38 12.04 i 13.32 12. iO 13.27 12.16 13.22 12.22 IS 19 14.12 12.71 j 14.06 12.77 14.01 12.84 13,95 12.90 19 20 14.86 13.38 ! 14.80 13.45 14.75 13.51 14.69 1 13.58 20 21 1 15.61 14.05: 15.54 14.12 15.48 14.19 15.42 14.25 21 22 16.35 14.72 ! 16.28 14.79 16.22 14.86 16.16 14.93 22 23 17.09 15.39 ! 17.02 15.46 16.96 15.54 16.89 15.61 23 24 17.84 16.06 17.77 16.14, 17.69 16.21 , 17.62 16.29 24 25 18.58 16.73 18.51 16.81 ! 18.43 16.89 1 18.36 16.97 25 26 19.32 17.40 19.25 17.48 i 19.17 17.57 ■ 19.09 17.65 26 27 20.06 18.07 19.99 18.15: 19.91 18.24 19.83 18.33 27 28 20.81 18.74 20.73 18.83 \ 20.64 18.92 20.56 19.01 28 29 21.55 19.40 21.47 19.50; 21.38 19.59 '21.30 19.69 29 30 22.29 20.07 22.21 20.17i 22.12 20.27 '22.03 20.36 30 31 23.04 20.74 22.95 20.84 22.86 20.94 22.76 ; 21.04 31 32 23.78 21.41 23.69 21.52 23.59 21.62 23.. 50 j 21.72 32 33 24.52 22.08 24.43 22.19 24.33 22.29 24.23 22.40 33 34 25.27 22.75 25.17 22.86 25.07 22.97 24.97 123.08 34 35 26.01 23.42 25.91 23.53 25.80 23.65 25.70; 23.76 35 36 26.75 24.09 26.65 24.21 26.54 24.32 26.44 1 24,44 36 37 27.50 24.76 27.39 24.88 27.28 25.00 1 27,17' 25.12 37 38 28.24 25.43 28.13 25.. 55 28.02 25.67 1 27.90 1 25.79 38 39 28.98 26.10 28.87 26.22 28.75 26.35 j 28.64 i 26.47 39 40 41 29.73 26.77 29.61 26.89 29.49 27.02 1 29.37! 27.15 40 30.47 27.43 30.35 27.57 30.23 27.70 30.11 27.83 41 42 31.21 28.10 31.09 28.24 30.97 28.37 30.84 28.51 42 43 31.96 28.77 1 31.83 28.91 31.70 29.05 31.58 29.19 43 44 32.70 29.44 32.57 29.58 32.44 29.73 32.31 29.87 44 45 33.44 30.11 33.31 30.26 33.18 30.40 33.04 30.55 45 46 34.18 30.78 34.05 30.93 33.91 31.08 33.78 31.22 46 47 34.93 31.45 1 34.79 31.60 34.65 3r.75 34.51 31.90 47 48 35.67 32.12 35.53 32.27 35.39 32.43 35.25 32.58 1 48 49 36.41 32.79 36.27 32.95 36.13 33.10 35 . 98 33.26 49 50 37.16 33.46 37.01 33.62 ^.86 33.78 36.72 .33.94 50 Dep. Lat. Dep. Lat Dep. Lat. Dep. Lat. 1 48 Deg. 1 471 Deg. 47^ Deg. 47i Deg. TKAVEKSE TABLE. 87 5' 51 42 Deg. m Deg. 42i Deg. 42| Deg. ~5l Lat. Dep. Lat. Dep. 34.29 Lat. Dep. Lat. Dep. 37.90 34.13 37.75 37.60 34.46 37.45 34.62 52 38.64 34.79 38.49 34.96 38.34 35.13 38.18 35.30 52 53 39.39 35.46 39.23 35.64 39.08 35.81 38.92 35.98 53 54 40.13 36.13 39.97 36.31 39.81 36.48 39.65 36.66 54. 55 40.87 36.80 40.71 36.98 40.55 37.16 40.39 37.33 55 56 41.62 37.47 41.45 37.65 41.29 37.83 41.12 38.01 56 57 42.36 38.14 42.19 38.32 42.02 38.51 41.86 38.69 57 58 43.10 38.81 42.93 39.00 42.76 39.18 42.59 39.37 58 59 43.85 39.48 43.67 39.67 43.. 50 39.86 43.32 40.05 59 60 44.59 40.15 44.41 40.34 44.24 40.. 54 44.06 40.73 60 61 45.. 33 40.82 45.15 41.01 44.97 41.21 44.79 41.41 62 46.07 41.49 45.89 41.69 45.71 41.89 '45.53 42.09 62 63 46.82 42.16 46.63 42.36 146.45 42., 56 146.26 42.76 63 64 47.56 42.82 47.37 43.03 147.19 43.24 ; 47.00 43.44 64 65 48.30 43.49 48.11 43.70 47.92 43.91 47.73 44.12 65 66 49.05 44.16 48.85 44.38 : 48.66 44., 59 148.47 44.80 66 67 49.79 44.83 49.59 45.05 49.40 45.26 49.20 45.48 67 68 50.53 45.50 50.33 45.72 50.13 145.94 49.93 46.16 68 69 51 .28 46.17 51.07 46.39 50.87 146.62 50.67 46.84 69 70 71 52.02 52.76 46.84 51.82 47.07 47.74 51.61 1 47.29 51.40 47.52 70 71 47.51 52.56 52.35 47.97 .52.14 48.19 72 53.51 48.18 ' 53.30 43.41 .53.08 48.64 .52.87 48.87 72 73 54.25 48.85 54.04 49.08 ,53.82 49.^2 53.61 49.-55 73 74 54.99 49.52 54.78 49.76 j 54.56 i 49.99 ■ 54.34 50.23 74 75 55.74 50.18 55.52 50.43 ' 55.30 | 50.67 1 55.07 50.91 75 76 56.48 50.85 56.26 51.10 1 56.03 ! 51.34 55.81 51.59 76 77 57.22 51.52 57 . 00 51.77 56.77 .52.02 56.54 ,52.27 77 78 57.97 52.19 57.74 52.44 i 57.51 52.70 57.28 52.95 78 79 53.71 52.86 58.48 53. 12 : 58.24 53.37 58.01 53.63 79 80 81 59.45 00.19 53.53 59.22 53.79 ij .58.98 | .54.05 54.46 !, ,59.72 154.72 58.75 54.30 80 81 54.20 59.96 .59.48 54.98 82 60.94 54. S 7 60.70 55.13 !, 60.46 55.40 60.21 .55.66 82 83 61. 6S 55.54 61.44 55.81 i|61.19 156.07 60.95 56.34 83 84 62.42 56.21 62.18 56.48 1 61.93 156.75 61.68 .57.02 84 85 63.17 56.88 62.92 57. 15!; 62.67 57.43 62.42 57.70 85 86 63.91 57.55 63.66 57.82 J63.ll 58.10 63.15 .58.38 86 87 64.65 58.21 64.40 53.50 64.14 .58.78 63.89 59.06 87 88 65.40 58.88 1 65.14 59.17 64.88 59.45 64.62 59.73 83 89 66.14 59.55 65. 8S 59.84 65.62 60.13 65.35 60.41 89 90 91 66.88 60.22 60.39 66.62 60.51 66.35 60.80 66.09 61.09 90 91 67.63 67.36 61.19 67.09 61.48 66.82 61.77 92 *.S.37 61.56 68.10 61.86 67.83 62.15 67.56 62.45 92 93 69.11 62.23 68.84 62.. 53 1 88.57 62.83 68.29 63.13 93 94 69.86 62.90 69.. 58 63.20, 69.30 63.51 69.03 63.81 94 95 70.60 63.57 70.. 32 63.87 70.04 64.18 69.76 64.49 95 96 71.. 34 64.24 71.06 64.55 70.78 64.86 70.49 65.16 96 97 72.08 64.91 71.80 65.22 71., 52 65.53 71.23 65.84 97 98 72.83 65.57 72.54 65.89 72.25 66.21 71.96 66.52 98 99 73.57 66.24 73.28 66., 56 72.99 66.88 72.70 67.20 99 100 1 74.31 66.91 74.02 67.24 Lat. 73.73 67.56 73.43 67.88 Lat. 100 5 Dep. Lat. Dep. Dep. Lat. Dep. 48 Deg. 47| Deg. 47h Deg 474 Deg. ss TEATT-FSi: ^AELT. g « i f ^ ~1 ^De^. ^Deg. j 43^D€^. ; ! 434 Deg. 2 Lat. D^p Lat Dep Lit. j Dep. ■' Lit Dep. ' *>.r3 0.68 0.73 0.39 ! 0.73! 0.6& 0.72 0.691 1 2 1.4S i.36 1.46 I..t7 i 1.45! 1.3^: 1.44! 1.38 1 2 3 2.19 2.05 2.19 2.06 2,18 2.07! 2.17 2.07 3 4 2-93 2.73 2.9i 2.74 2.90 2.751 2.89 2.77 4 5 3.6S 3.41 ; 3.64 3.43 3.63 3.44 1 3.61 3.46 5| 6 4.39 4.09 4.^J 4.11 4.35 4.13} 4.33 4.15 6 7 5.L2 4.7-7 ' 5.1^ 4. SO 1 5.08 4.82 [ 5.06i 4.84[ 71 8 5.S5 3.48 5.83 5.4^' 5.80 1 5.51; 5.78i 5.53 8 9 6.5S 6.14' 6.^3 5.17"; ■ 6.S5 ; 6.33! 6.2*> j 6.50 6.22! 9 I i 7.31 6.8> ' 8.041 i.oki 7.2s 7.25 1 6.88 ! 7.22 6 92 i 10 8.0: 7.54 i 7.99 ! 7.57 1 7.95' 7.61 ' li it S.T%[ S.IS\ 8.74 8.^.2 1 8.70 1 8.26 1 8.671 8.30! 12 13 9.5!" J*,^ ' 9.4''''' ?.^?i 9.43 ^ in 9.391 8.99. 13 £4 - ' : . .>.ii! 9.68 14 Ir .84 10.37 15 io ,_._ . . . : : 11.56 n.06| 16 17 i;2.43 1 ii.aaf 1 tA.b.3 i tt.-ia 13.06 ' 12.39 13.00 12.45 i IS i* 13.16 1 12.23 [ I3.ii! 12.33 19 13.90! 12.36 13. S4 ' : :7 S' i3.08 ; 13.72 13.14 19 20 i4.a3 13.64 14.. f 15.3J .. - 13.17 14. io 13.83 2i) *1 \ 15. 3o i4.32 ■ _ ^ ;; ^ 15. :7 14.52 2i ^ 16.09 \ 15. CW 1 S.&i i i5.vj*7 it5.!i*6U5.t4 13.89 15.21 22| 23 ; W.S% I0..53 15.7.S i, iS.TS 116.68 15.83 1 16. 6t 15.90; 23 24 17.5.5-; 1^.37 . 17.4- -^ i-': ♦7.41 16. .52 17. M 16.60 24 ->5 ts.2j*l 17.0.5:1 IS., -" - ; 3.13; 17.21 1 13.06 17.29; 25 2o 19.02 17.73 18. r. - :5.*'5 ' 17.?K> '' l^.T? !7.9S 29 27 19.75 [ l*.4i 19.^ - - - ; - , . - - ^ -^ ^ 2S 20. 4S 19.10 20..:: ; , ■ : ' 29 21.21 1 id. 78 2:l._, .:.:: , . ^ - ^ _ ; - _' : -- " , : , :* 30 2L.M'2d.46 21 .^a ; 22.. 5S .t *^-^^ ; 2i.70 j 2«>.65 ,1 i.i..^>7 2a.*.>| 30 22.57 ' 2i.L4 '2!. 24 i 2-? t9 2' . ?4 22 . 3** 21 .44 [ 3! y ;_ - ,_.*2|23.S ,. -: ; 22.13' 32 . - ,: 51 24..- , . 22.82 .33 S^ _..: , a. it:; 24.7: -. _. - ^ . ^ ^3,-:' ^ 35 %.3.d*J . -3.S7 '1 ',5.^ - ,3 . -ist r i'* - '■ 36 1 ^^.a3 24.55 ^o.\. ^6.11124 3* .- - , : ,- - .-^ - .-^ - ; : ~" -^4 25.^; ^- . ^-. -' . -^ ->r 3- 26.16 27.45 26.28 38 -^ 26.85 ■28.17: 28.97! 39 40 . -,^ . i 3 - ~ ■ - 7 - _ r. 1 27.53 28.^9 27.66 40 1 2^.^^ ^V - . - . - - - :>9.74:28.22 ^19.^2: 28.35: 41 in • r^f . 72 ' '^'^ . O-k o<-' . •" - :- 1- -^ -^ ■^"- n' 29.04: 42 i3 1 31.45 .:^.33|3i.S. ; .^ 29.74' 43 44 ► ^^ _ T ^ -•>,■:_ ^, .! ^^■^_.; ■ : 30.43 44 ' ' T " : ' ^ 31.12 i 45 T_ 31.81 ' 46 i; 32.50 47 - .T4;i ^^-A.; 34:..*2 j -^-^.^ . ^.67 , 33.19 j 48 ; . :3.42 35. :i5.54, 33.T3 3-5.40 -33.88 49 .y> .5-.. 5 7 34.10 ; 36.4.:. , o-z: . -V 36.37 1 34.42 j 33 . 12 ! 34.58 !50 1 i 1 l>ep. iL.. 1 ri^p. \ Lat. Dep- Sl.. Oep. Lat. 1 ! 1 ;' 47 C»e2. 1 461 Deg. ; 464 Def 464Deg. |E TK A VERSE TABLE. 89 1 51 1 43 Deg. 43i Deg. 43A Deg. 431 Deg. E 1 51 Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 37.30 34.78 37.15 .34.94 36.99 35.11 36.84 35.27 52 38.03 35.46 37.88 i 35.63 37.72 35.79 37.56 35.96 52 53 38.76 36.15 38.60 i 36.31 38.44 36.48 38.29 .36.65 63 54 39.49 3G.83 39.33 37.00 39.17 37.17 39.01 37.34 64 55 40.22 37.51 40.06 37.69 39.90 37.86 39.73 38.03 55 56 40.96 38.19 40.79 38.37 40.62 38.55 40.45 38.72 66 57 41.69 38.87 4i..52 39.06 41.35 39.21 41.17 39.42 57 58 42.42 39.56 42.25 39.74 42.07 39.92 41.90 40.11 68 59 43.15 40.24 •42.97 40.43 4:j.80 40.61 42.62 40.80 69 60 61 43. SS 40.92 43.70 141.11 43.. 52 41.30 41.99 43.34 44.06 41.49 60 61 44.61 41.60 44.43 41.80 44 . 25 42.18 62 45 . 34 42 . 28 45.16 142.48 44.97 42.68 44.79 42.87 62 63 46.08 42.97 45.89 43.17 45.70 43.37 45.51 43.57 63 64 46.81 43.65 46.62 43.85 46.42 44.05 46.23 44.26 64 65 47-. 54 44.33 47.34 44.. 54 47.15 44.74 46.95 44.95 65 66 48.27 45.01 48.07 145.22 147.87 45.43 47.68 45.64 66 67 49.00 45.69 48.80 45.91 48.60 46.12 48.40 46.33 67 68 49.73 46.38 49.53 46.59 49.33 46.81 49. i2 47.02 68 69 .50.46 47.06 50.26 47.28 ,50.05 47.50 49.84 47.71 69 70 71 51.19 .51.93 47.74 48.42 .50.99 47.96 I 50.78 4S.65 ; 51.50 48.18 .50.57 51.29 48.41 70 71 51.71 48.87 49.10 72 52.66 49.10 52.44 49.33 52.23 49.56 1 62.01 49.79 72 73 .53.. 39 49.79 i 53.17 50.02 52.95 50.25 52.73 ! .53.45 50.48 73 74 54.12 .50.47 153.90 50.70 53.68 50.94 51.17 74 75 54.85 51.15 154.33 51.39 54.40 51.63 54. 18 51.86 75 76 55 . 68 51.83 55.36 52.07 55.13 52.31 54.90 55.62 52.55 76 77 56.31 52.51 56.08 52.76 , 55.85 53.00 53.25 77 78 57.05 53.20 i 56.81 53.44 56.58 53.69 56.34 53.94 78 79 .57.78 53.88 ! 57.54 54.13 .57.30 54.38 1 57.01 54.63 79 SO 68.51 59.24 54.56 1 58 . 27 54.81 55.50 58.03 58.76 55.07 55.76 57.79 58.51 55.32 8'« 8J 55.24 159.00 56. Oi •i2 59.97 55.92 .59.73 .56.18 69.48 56.45 59.23 56.70 82 S3 60.70 .56.61 60.45 .56.87 60.21 57.13 .59.96 57.40 8-: 84 61.43 57.29 61.18 57.56 60.93 57.82 60.68 68.09 8o 85 62.17 57.97 61.91 58.24 61.66 58.51 61.40 58 . 78 8 86 62.90 58.65 62.64 58.93 62.-38 59.20 62.12 59.47 Sr. 87 63.63 .59.33 63.37 59.61 63.11 59.89 62.85 60.16 87 S8 64.36 60.02 64.10 60.39 63.83 60.. 58 63.57 60.85 8r 89 65.09 60.70 64.82 60.98 64.56 61.26 64.29 61.54 89 90 91 65.82 66.55 61.38 62.06 65 . 55 61.67 65.28 66.01 61.95 65.01 65.74 62.24 62.93 90 91 66.28 62.35 62.64 1 92 67.28 62.74 67.01 63.04 60 . 73 63.33 1 66.46 63.62 9£ 93 68.02 63.43 67.74 63.72 67.46 64.02 67.18 64.31 9? 94 68.75 64.11 68.47 64.41 68.19 64.71 1 67.90 65.00 9^* 95 69.48 64.79 69.20 65.09 68.91 65.39 68.62 65.69 9r. 96 70.21 65.47 69.92 65.78 69.64 66.08 69.35 66.39 96 97 70.94 66.15 70.65 66.46 70 . 36 66.77 70.07 67.08 97 98 71.67 66.84i 71.37 67.15 71.09 67.46 70.79 67.77 9'cl 99 72.40 67.52 72.11 67.83 71.81 68.15 71.51 68.46 99 100 5 73.14 68.20 72.84 68.52 72.54 68.84 72.24 Dep. 69.15 Lat. _100 i Dep. Lat. Dep. Lat. Dep. Lat. 47 Deg. 461 Deg. 464 Deg. 46:1 Deg. 90 TBAVEESE TABLE, o i 1 44 Deg. 44i Deg. 44^ Deg. 441 Deg. 45 Deg. c ST 9 Lat. Dep. Lat. Dep. Lat. Dep. 0.70 Lat. Dep. Lat. Dep. 0.72 0.69 0.72 0.70 0.71 0.71 0.71 0.71 0.71 1 2 1.44 1.39 1.43 1.40 1.43 1.40 1.42 1.41 1.41 1.41 2 3 2.16 2.08 2.15 2.09 2.14 2.10 2.13 2.11 2.12 2.12 3 4 2.88 2.78 2.87 2.79 2.85 2.80 2.84 2.82 2.83 2.83 4 5 3.60 3.47 3.58 3.49 3.57 3.50 3.55 3.52 3.54 3.54 5 6 4.32 4.17 4.30 4.19 4.28 4.21 4.26 4.22 4.24 4.24 6 7 5.04 4.86 5.01 4.88 4.99 4.91 4.97 4.93 4.95 4.95 / 8 5.75 5.56 5.73 5.58 5.71 5.61 5.68 5.63 5.66 5.66 8 9 6.47 6.25 6.45 6.28 6.42 6.31 6.39 6.34 6.36 6.36 9 10 7.19 6.95 7.16 7. '88 6.98 7.13 7.01 7.71 7.10 7.04 7.07 7.07 10 11 11 7.91 7.64 7.68 7.85 7.81 7.74 7.78 7.78 12 8.63 8.34 8.60 8.37 8.56 8.41 8.52 8.45 8.49 8.49 12 13 9.35 9.03 9.31 9.07 9.27 9.11 9.23 9.15 9.19 9.19 13 14 10.07 9.73 10.03 9.77 9.99 9.81 9.94 9.86 9.90 9.90 14 15 10.79 10.42 10.74 10.47 10.70 10.51 10.65 10.56 10.61 10.61 15 16 11.51 11.11 11.46 11.16 11.41 11.21 11.36 11.26 11.31 11.31 16 17 12.23 11.81 12.18 11.86 12.13 11.92 12.07 11.97 12.02 12.02 17 18 12.95 12.50 12.89 12.56 12.84 12.62 12.78 12.67 12.73 12.73 18 I 19 13.67 13.20 13.61 13.26 13.. 55 13.32 113.49 13.38 13.43 i;^43 14.14 19 20 14.39 13.89 14.33 15.04 13.96 14.26 14.02 .14.20 14.91 14.08 14.14 14.85 20 21 21 15.11 14.. 59 14.65 14.98 14.72 14.78 14.85 22 15.83 15.28 15.76 15.35 15.69 15.42 15.62 15.49 15.56 15.. 56 22 23 16.. 54 15.98 16.47 16.05 16.40 16.12 16.33 16.19 16.26 16.26 23 24 17.26 16.671 17.19 16.75 17.12 16.82 17.04 16.90 16.97 16.97 24 25 17.98 17.37!ll7.91 17.44 17.83 17.52 17.75 17.60 17.68 17.68 25 26 18.70 18.06: 18.62 18.14 18.54 18.22 18.46 18.30 18.38 18.38 26 27 19.42 18.7649.34 18.84 19.26 18.92 19.17 19.01 19.09 19.09 27 28 20.14 19.45 20.06 19.54 19.97 19.63 19.89 19.71 19.80 19.80 28 29 20.86 20.15 20.77 20.24 20.68 20.33 20.60 20.42 20.51 20.51 29 30 21.58 20.84 21.49 20.93 21.40 21.03 21.73 21.31 21.12 21.21 21.21 21.92 30 31 31 22.30 21.53 22.21 21.63 22.11 22.02'21.82 121.92 3'?, 23.02 22.23 22.92 22.33 22.82 22.43 22.73 22.53 122.63 22.63 32 33 23.74 22.92 23.64 23.03 23.54 23.13 23.44 23.23 23.33 23.33 33 34 24.46 23.62 24.35 23.72 24 . 25 23.83 24.15 23.94 24.04 24.04134 35 25.18 24.31 25.07 24.42 24.96 24.53 24.86 24.64 24.75 24.75135 36 25.90 25.01 25.79 25.12 25.68 25.23 25.57 25. 341! 25. 46 25.46 36 37 26.62 25.70 26.. 50 25.82 26.39 25.93 26.28 26.05 26.16 26.16 37 38 27.33i26.40 27.22 26.52 27. JO 26.63 26.99 26.75 26.87 26.87 38 39 28.05 27.09 27.94 27.21 27.82 27.34 27.70 27.46 27.58 27.58139 40 41 28.77 29.49 27.79 28.65 27.91 28 . 53 28.04 28.41 29.12 28.16 28.86 28.28 28.28 40 128,9941 28.48 29.37 28.61 29.24 28. 74 128.99 42 130.21 29.18 30.08 29.31 29.96 29. 4 29.83 29.57 129.70129.70142 1 43 130.93 29.87 30 . 80 30.00 30 . 67 30. 4 30.54 30.27jj30.41 30.41 43 44 31.65 30.56 31.52 30.70 31.38 30. H4 31.25 30.98 31.11 3l.68ll31.82 31.11 44 45 32.37 31.26 32.2.^ 31.40 32.10 31. r4 31.96 31. 8S l45 46 33.09 31.95 32. 9S 32.10 32.81 32. '.4 32.67 32. 38i|32. 53132. 53i46 47 33.81 32.65 33.67 32.80 33.. 52 32.^4 33.38 33.09 33. 23;33. 23,47 4H 34.53 33.34 34.3? 33.49 34.24 33.fi4 34.09 33.79 ,33.94 33.94 48 49 135.2.'= 34.04 3d.lC 34.19 .34.95 34.:^4 34.8C 34.50 34.65 34,65149 1 50|35.9'/ '34.73 35.85 ►34.89 35.66 Dep. 35.05|,35.51 35.20 35.36 35. 3f 5 50 6 o c S Uep. Lat. Den. 1 Lat. Lat. Dep. Lat. Dep. 1 Lat. i i 46 Tleg i 45 f Deg. 1 .5; Deg. 4Si Deg. 45 Deg. TRAVEBSE TABLE. 91 A TiBLE OF XATURAL SIXES. '■) L>e-, 1 Uey. Dez. Nil. >. Co-s N-:. ^V. Cg- M ?i~e Si-e n Si^^ sine 0*}-ji» Cnit, ■45 999S5'0S-; Uej. >i-. \ r -- ---■- ■^ - -- - • ' 4 L^ez- y^_ N. C> - ---r ; SLjae M ~« QOTn-? «0 ■ - ,-. - - 34 ' > >4., .S6 -746 55 744 -54 4-:: .>3 •"" i'* ?2 :io 4-5 "23 44 2143 -1942 rL^4t :I4;40 1239 1.) • i -5 ^ - : ■ - ' ; : , 13 _ - ; I 6 5 j "fins' Stir . ;-;:'?l 99940 Na:. 0.:,..., — . 7 • - " 2 7S ; 99t?22 T ■ Co- ' Na:. yi i 69 De?. •:■: T'-r, ■' D-z- :-: ^^r- 75Deg. : A TABLE OF T^^ATUKAL fil^ES. 93 M N. S. I N. CS. 5 Deg. 037161 08745 1 08774 08803 08831 0S860 08889 08918 08947 08976 09005 09034 ogoG?" 09092 09121 09150 16109179 17109208 18109237 19 09268 20109295 21J09324 22 1 09353 23:09382 99619 99617 99614 99612 99609 99607 99604 99602 99599 99596 99594 99591 99588 99586 99583 99580 6 Deg. 09411 09440 09469 09498 09527 09556 09585 09614 09642 •)9671 09700 097?;" 09758 09787 09316 09S45 09874 09903 09932 09961 09990 .10019 99578: 99575 995721 995701 99567! y9ob4 99562 99559 99556 99553 99551 99548 99545 99542 99540 99537 99534 99531 99528 99526 99523 99520 99517 99514 99511 99508i 995061 99503 99500 99497 N.S . 10453 10482 10511 10540 10569 10597 10626 10655 10684 10713 10742 10771 10800 10829 10858 1088 7 10916 10945 10973 11002 li03i 11060 11089 11118 11147 11176 11205 11234 11263 11291 1132 11349 11378 11407 11436 11465 11494 116-^3 11552 11580 11609 11638 11667 11696 11725 11754 CS. 99^02 99399 99396 99393 99390 99086 99383 99380 99377 99374 99370 99367 99364 99360 99357 99354 99351 99347 99344 99341 99337 9334 99331 99327 99324 89320 99S17 ^9314 99310 99307 N. CS. N. S. Dei 8 Deg. N.S. 12187 12216 12245 12274 12302 12331 12360 12389 12418 12447 12476 12504 12533 12562 12591 12620 N. CS . : 99255 99251 99248 99244 99240 14033 99237l|14061 992331114090 99230114119 99226|14148 99222 114177 99219 99215 99211 99208 14205 14234 14263 14292 99204 114320 99200 114349 12649 99197 12678;99193 12706 99189 12735 12764 12793 12861 12880 12908 13937 12966 12995 13024 13053 )9303 99300 99297 99293 99290 99286 99283 99279 99276 99272 99269 99265 99262 99258 N.CS. 1 N.S. |!N. CS, 99186 99182 99178 99175 99171 99167 99163 99160 99156 99152 99148 99144' 14378 14407 14436 14464 14493 14522 14551 14580 14608 14637 14666 14695 14723 14752 14781 84 Deff. 83 De^. 82 Deg. 14810 14838 14867 14896 14925 14-954 14982 15011 1 5040 15069 15097 15126 15155 15184 15212 15241 15270 15292 15327 15356 15385 15414 15442 15471 15500 15529 15557 15586 1561 5 N. CS. N. CS. 990271115643 990231116672 99019il57Cl 990151 15730 990111 15758 98961 16103 989571116132 98953!il6i60 98948il6189 98944516218 98940 116246 98936 98931 98927 98923 98919 98914 98910 98906 98902 98832 98827 98823 98818 98814 98809 98805 98800 98796 98791 98787 98782 98778 98773 N.S. 81 Deg. 98769 98764 98760 98755 98751 98746 98741 98737 98732 98728 98723 98718 98714 98709 9S704 98700 16620J98609 16964 16992 17021 17050 17078 17107 17136 17164 N.CS. I N.S. 80 i)eg. ?4 A r.*ELE CF ^ATVRJlL Sl^Ei I lU ue^. 11 De, 13 Der. U Der M' N 5 N c* xs ; 14: 17766 »h4a»9 1&4^?- 15 i77M&>4i>4 19-5"3 5«.l ^ 51 5- 1^ 53 :^ 54 -^ N. < N. Ojj. 74.X' 2413' r 7444 -24. f _ -^ Dez- A TABLE OF ?«ATURAL SINES. 95 15 Deg. 25882 25910 25938 25966 25994 26022 26050 26079 26107 26135 96593 96585 96578 96570 96562 96556 96547 96540 96532 96524 26163 96517 26191 122621! 26R47 26275 26303 96509 96502 96494 96486 96479 16|26331 9647] 17,28359196463 18;26387!96456 19|26415i96448 20 28443196440 21 26471196433 22 26500! 96425 26528! 964 17 2655698410 2658496402 26612 96394 2664096386 28|26668|96379 29 26696 96371 30 26724 96363 31126752 32126780 33 1 26808 34| 26836 3526864 36126892 37j26920 16 Deg. N.S. 27564 27592 27620 27648 27676 27704 27731 27759 27787 27815 27843 27871 27899 27927 27955 27983 28011 28039 28067 28095 28123 28150 28178 28206 28234 28262 28290 28318 28346 28374 128402 N. CS . 96126 96118 96110 96102 96094 96086 96078 96070 96062 96054 96046 96037 96029 96021 96013 96005 9599 95989 95981 95972 95964 95956 95948 95940 95931 95923 95915 95907 95898 95390 95882 96355 96347 96340 96332 96324 96316 ,96308 38126948 96301 39,26976 96293 402700496285 41127032 96277 42:2706G!96269 43 27088'96261 44 27116;96253 45127144196246 46127172 96238 47'27200 96230 48; 27228 196222 49i27256;96214 50:27284 96206 51127312 96198 52 27340196190 53 27368196182 96174 96166 96158 96150 96142 96134 N. S. 54:27396 55127424 56 27452 67127480 58 27508 ^927536 28429 28457 28485 28513 28541 28569 28597 28625 28652 28680 28708 28736 28764 28792 28820 17 >eg. N.S. 29237 29265 29293 29321 29348 29376 29404 29432 29460 29487 29515 29543 29671 29599 29626 29654 95630 95622 95613 95605 95596 95588 95579 95571 95562 95654 95545 95536 95528 95619 95511 95502 95874 958651 95857 95849 95841 95832 95824 95816 95807 95799 95791 95782 95774 95766 95757 14 Deo-. 128847 ,28875 123903 i2S93 J28959 I2S987 '29015 i29042 129070 129098 129126 29154 ;29182 129209 29682 29710 29737 29765 29793 29821 29849 29876 29904 29932 29960 29987 30015 30043 3 0071 30098 30126 30154 30182 30209 30237 30265 30292 30320 30348 30376 30403 30431 30459 30486 N.CS. 95493 95486 95476 95467 95469 95450 95441 95433 95424 95415 95407 95398 95389 95330 95372 95383 95354 95345 95337 9532 95319 95310 9530 95293 955^4 95275 95266 95257 95248 95240 957491130514 95740i;30542 95732i30570 95724,3059 95715i!30625 957071130653 N. CS. 95698 95690 95681 95673 95664 95656 95647 956391 30680 30708 30736 30783 30791 30819 95231 95222 95213 95204 95195 95186 18 Deg. 19 Deg. 31344 31372 31399 31427 31454 31482 31510 3153 31565 31593 31620 31648 31675 31703 31730 31758 31786 31813 31841 31868 31896 31923 3195 31979 32006 32034 32061 32089 32116 32144 N.CS. 95106 95097 96088 96079 96070 96061 95052 95043 95033 95024 95015 95006 94997 94988 94979 94970 94961 94952 94943 94933 94924 94915 94906 94897 94888 94878 94869 94860 94851 94842 94832 94823 94814 94805 94795 94786 94777 94768 94758 94749 94740 94730 94721 94712 94702 94693 N.S. ' 32557 32584 32612 32639 32667 32694 32722 32749 32777 32804 32832 32859 32887 32914 32942 32969 N.CS. 94552 94642 94533 94623 94614 94504 94495 94485 94476 94466 94457 94447 94438 94428 94418 94409 32997 33024 33061 33079 33106 33134 33161 33189 33216 33244 33271 33298 33326 33353 33381 32171 32199 32227 322.54 32282 32309 95177 32337 96168 95159! 95150 95142 95133 :J4884 94874 94665 9465G 94648 94837 94627 32364 94618 32392 :94609 32419 94599 N. 8. 73 i^ecr. 30846:95124 30874 95115 N. CS. I N.S. . 72 Deer. 32447 32474 32602 32529 N. CS. I N. S, 94'^90 94580 94571 9456 1 71 Dc 33408 33436 33463 33490 33518 33545 33573 33600 33627 33655 33682 33710 33737 33764 33792 94399 94390 94380 94370 94361 94351 94342 94332 94322 94313 94303 94293 94284132 94274 31 94264 30 94254 94245 94235 94225 94215 94206 94196 94186 94176 94167 94157 94147 94137 94127 94118 33819 33846 33874 33901 33929 33956 33983 34011 34038 34065 34093 34120 34147 34175 94108 94098 '94088 194078 194068 94058 ; 94049 94039 94029 94019 94009 93999 93989 93979 27 26 25 24 23 22 21 20 19 i^i 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 N.CS.! N.S. IM 70 Df yti A TABLE OF TSATURAL SINES. 20 Ueg. I 21 Deg. N. S. I N. CS. t 'NTiT I N. csT 35837 193353 35864193348 35891 93337 M[ G'34202'93969 1,' 34229, 93959; 2 34257 1 93949 3:34284i93939 4134311 93929' 5134339:93919 6|343G6, 93909 7!34393'93S99 8,34421 9388 9 9134448 93879: 10{34475 93869: 11134503 93859! 12134530 93849' 13 34557 93839: 14 34584.93829^ 1513461293819 ii2 Deo-. 23 Deg. i 24 Deg. N.S. IN. CS. / N.S. IN. CS. j i\. S. 359i8 35945 35973 36000 36027 36054 93327 93316 93306 93295 93285 93274 36081 {93264 36108193253 36135 93243 36162ly3232 36190193222 36217 93211 3624493201 16134639 93809 17134666:93799 18134694:93789 19|34721;93779 20;34748|93769 2l!34775i937o9 22134803 93748 23 34830 93738 24134857 93728 25,34^84' 937 IS 26;349i'^ 93708 27134939 93698 28:34966 93688 29134993 93677 30 i 35021 93667 31 i 35048 93657 32 35075 93647 33i35l02'93637 34135130:93626 35135157:93616 36:35183 93606 37 35211193596 38 ,35239! 93585 39:35266193575 40 35293:93565 41 35320 1 93555 42 35347 93544 43: 35375I 935.34 4435402:93524 45; 35429 93514 46135456193503 47 35484193493 48i 3.551 1193483 49:35538 93472 50 1 35565 93462 51 135592' 93452 52!3.56l9i9344l 53,35647:93431 54! 35674 9.3420 55135701 93410 56! 35728 93400 571357.55 93389 58135782:93379 59! 35810, 93368 M"'; N. CS. i N. S. |~"69~De^. 36271193190 36298193180 363::5|93169 3635 36379 36406 36434 36461 93159 93148 93137 93127 93116 36488193106 36515 93095 36542:93084 3656y{93074 36596 93063 36623 93052 36650 j 93042 36677193031 36704|93020 36731 93010 3675S|92999 36785192988 368 1 2 36839 36867 36894 36921 3694S 36975 92978 92967 92956 92945 92935 92924 9291 37002 92902 37029 ;92892 37050192881 37461 i37488 137515 137542 137569 37595 : 3782 2 |37649 137676 37703 37730 37757 37784 37811 37838 37865 : 927 IS 192707 192697 192686 192675 192664 i92653 ; 92642 192631 ,92620 ,'92609 (92598 :9258? 192576 i92565 [ 92554 37892J 92543 379l9l92.532 37946192521 37973192510 37999 38026 38053 3>080 3? 107 3M34 .38161 38188 38215 38241 38268 92499 92488 92477 92466 92455 92444 92432 92421 92410 92399 92388 38295 3S322 138349, 38376' 3S403 38430 38456 384S3! ,38510. 38537 38564 38591 38617 38644 38671 92377 92366 92355 92343 92332 92321 92310 92299 92287 92276 92265 92254 92243 92231 92220 39073 39100 39127 39153 39180 39207 39234 39260 39287 39314 39341 39367 39394 39421 39448 39474 39501 39528 39555 39581' 39608i 39635 39661; 39688 39715; 39741' 39768 39795- 39822' 39848 39875 39902 39928 399.55 ; 39982 ; 40008 140035 140062 j 40088 40115 4014 '40168 40195 40221 I 40248' : 40275 92059 '92039 :9202s ! 920 16 192005 91994 91982 :91971 |919.59 91948 '91936 91925 91914 '91902 J91891 191879 ;91S68 91856 ^91845^ '91833 ! 9 1822 91810 i91799 91787 91775 91764 91752 91741 91729 91718 91708 91694 91683 91671 91660 91648 91636 91625 91613 91601 91590 9157 91566 91555 91543 91531 40674 40700 40727 40753 40780 40S06 40833 40860 40886 40913 ■40939 40966 40992 41019 41045 41072 4'l098 41125 41151' 41178^ 41204 41231 41257 41284 41310 41337 41363 41390 41416 41443 41469 ;NXS.|>£ 9 1355 i 60 9 1.343 1 59 91331 |58 91319 57 91307i56 91295155 9 1283; 54 91272 53 91260 52 91248 51 91236(50 91224:49 91212:48 91200 ' 91188 4b 91176 45 91164 44 91152 43 9114042 91128!4i 91116140 91104139 91092:38 91080:37 91068 3b 91056|35 91044 34 9 1032 33 9 1020 '32 91008|31 90996130 68 Deg. . 67 Peg A 1"A15L£ 01' NATURAL SINES. 97 Des. 42262 9U631 42288 90618 2'42315 90606 3142341 190594 4'42367j90582 5 42394! 90569 90557 90545 90532 90520 6! 42420 7.42446 8 '42473 9;42499 10.42525!90507 lli42552'90495 12 42578190483 13:42604190470 14 4263l|90458 15 42657 1 90446 16 42683'90433 17i42709'90421 18;42736|90408 19|42762!90396 20 142788 190383 21j42815i90371 22 42841190358 23 42867190346 24142894 90334 25142920 90321 26142946190309 27142972 90296 28^42999190284 29143025190271 30,43051190259 26 Deg. 43837 43863 43889 43916 43942 43968 43994 44020 44046 44072 44098 44124 44151 44177 44203 44229 44255 44281 44307 44333 44359 44*385 44411 44437 44464 44490 44516 44542 44568 44594 44620 31143077190246 32,43 104190233 33143130 90221 34143156 90208 35i43182!90l96 36 43209190183 37i43235'90l71 38 4326li90l58 39 43287190146 40 43313!90133 41143340190120 42i43366|90l08 43:43392190095 44 43418 45: 43445 46:43471 47143497 48143523 49143549 50 '435 75 51143602 52143628 53i43654 54143680 55;43706 56143733 57143759 58 1 43785 59 43811 M N.CS. 90082 90070 44646 44672 44698 44724 44750 44776 44802 44828 44854 44880 44908 44932 44958 44984 45010 90057 90045 90032 90019 90007 89994 89981 89968 39956 89943 89930 89918 89905 89892! N. S. 64 D( I N. CS . i 898791 89867! 89854 89841 89828 89816 S9803 89790 89777 89764 89752 89739 89726 89713 89700 89687 89674 89662 89649 89636 89623 89610 89597 89584 89571 89558 89545 89532 89519 89506 894931 S9480 894671 89454! 894411 89428 { 89415 39402 1 89389! 89376! 89101 89087 89074 89061 89048 89035 89021 89008 88995 88981 88968 88955 88942 88928 88915 88902 45036 45062 45088 45114 45140 45166 45192 45218 45243 45269 45295 45321 45347 45373 46201 46226 46252 46278 46304 46330 48355 46381 46407 89363;|46433 89350JI46458 89337!i46484 89324!!46510 89311 ''46538 892981: 46561 8'9285[j46587 8927214661 89259J46639 89245!|46664 89232i|46690 89219146716 89206|i46742 89193!i46767 891801146793 891671:46819 89153:46844188349 89140! 46870i88336 N.CS. !28 Deg. N. 1 N.CS. 4694788295 46973 88281 46999 47024 47050 47076 47101 47127 47153 47178 47204 47229 47255 47281 47306 47332 47358 47383 47409 47434 47460 47486 47511 47537 47562 47588 47614 47639 47665 47690 47716 47741 47767 47793 47818 47844 47869 S95 47920 47946 47971 47997 48022 48048 48073 48099 N.CJ 89127! 89114 46896188322 46921188308 N.CS. 1 N.i 63 Deg-. li 62 De^ 48124 48150 48175 48201 48226 48252 88267 88254 88240 88226 88213 88199 88185 88172 88158 88144 88130 117 88103 88089 88075 88062 88048 88034 88020 88006 87993 87979 87965 87951 87937 87923 87909 87896 87882 29 Deg. N.S. iN. CS. !M 87868 87854! 87840! 87826' 87812 87798 87784 87770 87756 87743 87729 87715 87701 87687 87673 48481 48506 48532 48557 48583 48608 48634 48659 48884 48710 48735 48761 48786 48811 48837 48862 48888 48913 48938 48964 489S9 49014 49040 49065 49090 49116 49141 49166 49192 49217 49242 87659 87645 87631 87617 87803 87589 49268 49293 49318 49344 49369 49394 49419 49445 49470 49495 49521 49546 49571 49596 49822 49647 49872 87462 60 87448,59 8 743 i 58 87420 57 87406:56 87391155 87377154 87363:53 87349|52 87335 51 87321 50 87306 '49 87292'48 87278147 87264'46 87250;45 87235:44 87221143 87207:42 8719341 8717SJ40 8716439 8715038 87136-37 87121136 87107:35 87093 '34 87079 33 87064132 8705031 7036 30 29 28 27 26 48277 87575 4 8303 '87561 48328187548 48354187532 48379 18751 8 48405 18 7504 48430 48456 N. cs: 87490 87476 87021 87007 86993 86978 86964 25 86949 23 22 21 20 19 18 17 16 86935 86921 86906 86892 86878 86863 86849 86834 868201 15 86805 86791 61 Dejr. 4989786777 49723:86762 49748!86748!l0 9 8 7 6 5 4 3 2 1 4977386733 49793,86719 4982486704 49849 86690 49874 86675 49899 86661 49924, 8664f5 49950 86632 49975I86617 N.CS. I N.S. 60 Deg. 98 A T.\:bLE of NATUKAl* SINES. 30 Di 31 Deg 33 Deg. N. CS, 50000i86603 50025186588 50050 ! 865? 3 50076186559 50101186544 50126J86530 50151 86515 50176:86501 50201 186486 50227 50252 50277 50302 50327 50352 86471 86457 86442 86427 86413 86398 50377186384 34 Deg. N. S. I N. OS. !55919|82904 ;55943:82887 155968182871 155992182855 J56016'82839 '56040 82822 |560648280& 156088:82790 156112 82773 156136:82757 i56l60|82741 i56l84;82724 '56208:82708 :56232{82692 156256 82675 :5628082659 50403| 86369 50428186354 504531 86340 50478 86325 50503 86310 50528186295 50553j86281 50578186266 50603:86251 50628 86237 50654 86222 50679186207 50704186192 5072986178 50754 | 86163 50779186148 50804 86133 50829 50854 50879 50904 5092 50954 50979 51004 83276 83260 83244 5^5436183228 55460133212 5548483195 55509; 83 179 840881 15558 lj83 131 84072 !^55605l831 15 84057,55630183098 84041155654 83082 84025 55678 183066 84009 1 55702:83050 83994 55726[83034 83978 !>55750:83017 83962155775183001 839461 55799|82985 839301:55823182969 83915 1:55847|82953 5441 5 183899 II55871 82936 54440 '83883 '' 55895 82920 IIN. CS. I N 56305 56329 56353 56377 56401 56425 82643 82626 82610 82593 82577 82561 56449 82544 56473j82528 5649782511 56521 82495 56545 82478 56569 82462 5659382446 56617 82429 5664l|82413 .56865182396 !56689'82380 {56713182363 156736182347 J5676082330 '56784182314 [56808 |56832 58B56 56880 56904 82297 82281 82264 82248 82231 :56928 82214 !56952!82198 ;56976|82181 15700082165 i57024 157047 157071 J57095 :57li9 ;57143 57167 57191 57215 57238 57262 57286 57310 57334 82143 14 82132113 182115 12 '82098111 32032 82065 82048 82032 820 1 5 81999 81982 81965 81949 81932 56 Deg. N. CS. I N. S . 53 Deg.' A TABLE OF NATURAL SIKES. 99 35 Deg. N. S. 57358 57381 57405 57429J81865 N. CS. 81915 81899 81882 57453 57477 57501 57524 57548 57572 57596 57619 57643 57667 57691 57715 16157738 17157762 18 57786 57810 57833 81848 81832 81815 81798 81782 81765 81748 81731 81714 81698 81681 81664 81647 1631 81614 81597 81580 57857i81563 57881 81546 81530 81513 81496 57904 57928 ;57952 26|57976i8l479 27157999 81462 28'58023i8l445 29158047:81428 30158070 81412 81395 81378 81361 36 Deg. IV. s. 58779 58802 58826 58849 58873 58896 58920 58943 58967 58990 59014 59037 59061 59084 59108 59131 59154 59178 59201 59225 59248 59272 59295 59318 159342 59365 59389 59412 59436 59459 59482 3 1 158094 32 58118 3358141, 34:58165 SI 344 35J58189 S1327 36158212 81310 37158236 81293 38 5826081276 39:58283 81259 40,58307181242 4ii58330|81225 42158354 81208 43158378 81191 44 58401181174 45 58425 81157 46 58449 47i 58472 48! 58496 49 58519 50 58543 51|58567 52158590 53158614 54 58637 55 58661 56 58684 57158708 58158731 59 58755 N.CS, 81140 81123 81106 81089 81072 81055 81038 81021 81004 80987 80970 80953 80936 80919 N.8. 54 Deg. 59506 59529 59552 59576 59599 59622 59646 59669 59693 59716 59739 59763 59786 59809 59832 N.CS. 809021 80885 80867 80850 80833 80816 80799 80782 80765 80748 80730 80713 80696 80679 80662 80644 80627 80610 80593 80576 80558 80541 80524 80507 80489 S0472 80455 80438 80420 80403 S03S6! S03681 S0351 S0334 80316 80299 80282 80264 80247 80230 37 Deg. n:s7~"n. CS. 60182 60205 60228 60251 60274 60298 60321 60344 60367 60390 60414 60437 60460 60483 60506 60529 79864 79846 79829 79811 79793 79776 79758 79741 79723 79706 79688 79671 79653 79635 79618 79600 59856 159879 159902 59926 159949 59972 80021 59995 80003 60019 79986 60042 79968 60065:79951 60089 '79934 60]12'79916 60135 79899 60 '58179881 60553 60576 60599 60622 60645 60668 60691 60714 60738 60761 60784 60807 60830 60853 60876 60899 60922 60945 60968 60991 61015 61038 61061 61084 80212l|61107 80195 61130 80178,161153 80160!!61176 801431:61199 80l25 !i61222 80l08j 80091i 800731 80056 80038 [61245 1 6 1268 161291 ,61314 161337 161360 79583 79565 79547 79530 79512 79494 79477 79459 79441 79424 79406 79388 79371 79353 79235 79318 79300 79282 79264 79247 79229 79211 79193 79176 79158 79140 79122 79105 79087 79069 61566 61589 61612 61635 61658 61681 61704 61726 61749 61772 61795 61818 61841 61864 1887 61909 79051 79033 79015 78998 78980 78962 3ii Deg. N.S. 61383 78944 61406 78926 :61429'78908 161451 78891 ''6147478873 61497,78855 ii6l52078837 1161543 78819 61932 61955 61978 62001 62024 62046 62069 62092 62115 62138 62160 62183 62206 62229 6225 L 62274 62297 62320 62342 62365 62388 6241 62433 62456 62479 62502 62524 62547 62570 62592 62615 62638 fi2660 62683 N.CS. 78801 78783 78765 78747 78729 78711 78694 78676 78658 78640 78622 78604 78586 78568 78550 78532 78514 78496 78478 78460 78442 78424 78405 78387 78369 78351 78333 78315 78297 78279 7 8261 78243 78225 78206 78188 78170 78152 78134 78116 78098 78079 78061 78043 78025 78007 77988 39 Deg. N.S. IN.CS. M 62932 62955 62977 63000 63022 63045 63068 63090 63113 63135 63158 63180 63203 63225 63248 63271 63293 63316 63338 63361 63383 63406 63428 63451 63473 6^496 63518 63540 63563 63585 63608 63630 63653 63675 63698 63720 63742 63765 63787 63810 63832 63854 63877 63899 63922 63944 77970 77952 77934 77916 N. CS. 1 N. S. I N. CS. 1 N. S. 53 Deg. 52 Deg. 62706 177897 62728177879 62751 77861 62774 77843 62796 77824 62819177806 62842 77788 2864 77769 62887 77751 N. CS. I N.S. 51 D 77715 77696 77678 77660 77641 77623 77605 77586 77568 77550 77531 77513 77494 77476 77458 77439 77421 77402 77384 77366 77347 77329 77310 77292 77273 77255 77236 77218 77199 77181 77162 77144 77125 77107 77088 77070 77051 77033 77014 76996 76977 76959 76940 76921 76903 76884 63966 63989 64011 64033 64056 64078 64100 64123 64145 64167 64190 64212 64234 64256 76866 76847 76828 76810 76791 76772 76754 76735 76717 76698 76679 76661 76642 76623 N. CS. 1 N.S. "~50 beg"" 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2, 1 100 A TABLE OF NATURAL SINES. 10 11 12 13 14 15 16 17 18 19 20 21 22 •23 24i 25 20 27 28 29 30 31 32 33 34 35 36 37 I 38 39 I 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 58 59 60 M 40 Deg. N. S. 64279 64301 64323 64346 64368 64390 64412 64435 64457 64479 64501 64524 64546 64568 64590 64612 64635 64657 64179 64701 64723 64746 64768 64790 64812 648S4 64856 64878 64901 64923 64945 4967 64989 650 li fi5033 65055 65077 65099 65122 65144 65166 65188 65210 5232 65254 65S76 65298 65320 65342 65364 65386 65408 65430 65452 65474 65496 65518 65540 65562 65584 6560 6 N. r.^. N.CS. 76604 76586 76567 76548 76530 76511 76492 76473 76455 76436 76417 76398 76380 7636 i 76342 76323 76304 76286 76267 ^48 76229 76210 76192 76173 76154 76135 76il6 76097 76078 76059 76041 41 Deg. N.S . 65606 65628 65650 65672 65694 65716 65738 65759 6578 65803 65825 65847 65869 65891 659] 3 65935 65966 65978 66000 66022 66044 66066 6608H 66109 6613 1 66153 66175 66197 66218 66240 66202 . A' :c2 166284 6003 66306 75984 66327 75965! 66349 75946' 6637! 75927 i 66393 75908-66414 75889:86436 75870!66458 38511 66480 758321 66501 75813:66523 75794 66545 75775r66566 75756r;66588 N, CS. 75471 75452 42 Deg. N.S. IN.CS. 66913 74314 66935 5738 66610 5719 66632 75699|'66653 75680|66675 7566166697 75642ii66718 75623i; 66740 75604166762 755851166783 755661! 66805 75547166827 75528 75509 75490 75471 N.S. 49 D( 75433:66956 75414166978 753951166999 75375 67021 753561167043 75337|| 67064 75318ii67086 75299:167107 75280 75261 75241 75222 67129 !67151 1 67 172 67194 75203=67215 75184 !i 67237 75165 75146 75126 75107 75088 750R9 75050 75030 75011 74992 74973 74953 74934 74915 7489 6 74876 74857 4838 74S18 74799 74780 74760 74741 74722 74703 74683 74664 74644 74625 74808 74586 74567 74548 74528 74509 74489 74470 74451 74431 74412 74392 66848 74373 66870 74353 66891 74334 66913 74314 N.CS. I N.S. 67258 167280 16730] 67323 67344 67366 67387 67409 67430 67452 67473 67495 S7516 67538 67559 .^7580 67602 i7623 ■i7645 ^7668 "^7688 o7709 67730 •.H7752 'W773 ";7795 •■7816 67837 67859 67880 67901 67923 67944 67965 67987 88008 68029 68051 68072 68093 68115 68136 48 Deg. 74296 74276 74256 74237 74217 74198 74178 74159 74139 74120 74100 74080 74061 74041 74022 74002 73983 73963 73944 73924 73904 73885 73865 73846 7:^826 1 73806 i 73787! 73767' 73747^ 73728 43 Deg. N.S. 68200 68221 68242 68264 68285 68306 68327 68349 68370 68391 68412 68433 68455 68476 68497 68518 73708 73688 73669 73649 73629 73610 73590 73570 3551 73531 73511 73491 73472 73452 73432 73412 73393 73373 73353 73333 73314 73294 73274 73254 73234 7321 73195 68157 73175 68179173156 68200173135 N.S, 47 Den-. 168639 68561 68582 68603 68624 68645 68666 68688 68709 68730 68751 68772 68793 68814 68835 68857 68878 68899 68920 68941 68962 68983 69004 69025 69046 69067 69088 N. CS. 73135 73116 73096 73076 73056 73036 73016 72996 72976 72957 72937 72917 72897 72877 72867 72837 72817 72797 72777 72767 72737 72717 72697 72677 72657 72637 726 i 7 72597 72577 72557 72537 44 Peg. N. S. N. CS. 72517 72497 72477 72457 72437 72417 72397 7237r 72367 72337 72317 72297 69109 72277 69130 69151 172 69193 69214 69235 69256 69277 69298 69319 69340 69361 69382 69403 69424 69445 69468 72257 72236 N.CS. 72216 72196 72176 72156 72136 72116 72095 72075 72055 72035 72015 71995 71974 71954 7193 4 N. s! " 46 beg. 69466 69487 69508 69529 69649 69570 69591 69612 69633 69654 6967 69696 69717 69737 69758 69779 69800 69821 69842 69862 9883 69904 f'9925 69946 69966 69987 70008 70029 70049 0070 70091 70112 70132 70153 70174 70195 70215 70236 70257 70277 70298 70319 70339 70360 70381 70401 71934 71914 71894 71873 71853 71833 71813 71792 71772 71752 71732 71711 71691 71671 71650 71630 71610 71690 71569 71649 71529 71508 71488 71468 71447 71427 71407 71386 71366 71345 71325 71305 71284 71284 71243 71223 71203 71182 71162 71141 71121 71100 71080 71059 71039 71019 70422 70998 70443 70978 70463 70957 70484 70937 70505170916 70525:70898 70646: 70876 70567 70866 70687 70834 70608170813 70628 70793 70649 70772 70670 70752 70690170731 70711170711 N.CS. I N.S. 45 Deg. t ^Sc J 6 4a^ LIBRARY OF CONGRESS 019 408 620 9 ^li!' ( r ii«air- »'-;^ ■ ■■immw